Natural Logarithms Defined as Integrals: Introduction by mes

hive-128780 · @mes · Mar 27 '20 (edited)

$2.39

Natural Logarithms Defined as Integrals: Introduction

https://youtu.be/M-N2PQ5UZns

In this video I go over logarithms but this define natural logarithms using integrals through the Fundamental Theorem of Calculus. In my previous videos I went over the definition of the logarithm as an inverse to the exponential function but the definition I go over in this video is more concrete and better suited when dealing with derivatives and integrals.

---

Watch Video On:

- DTube: [https://d.tube/#!/v/mes/a77jni9w6uw](https://d.tube/#!/v/mes/a77jni9w6uw)
- BitChute: [https://www.bitchute.com/video/4CKkwspA8RGK/](https://www.bitchute.com/video/4CKkwspA8RGK/)
- YouTube: [https://youtu.be/M-N2PQ5UZns](https://youtu.be/M-N2PQ5UZns)

Download Video Notes: https://1drv.ms/b/s!As32ynv0LoaIg4I9_IzTxQXB9sY_KQ?e=QOOgWk

---

# View Video Notes Below!

---

>Download these notes: Link is in video description.
>View these notes as an article: https://peakd.com/@mes
>Subscribe via email: http://mes.fm/subscribe
>Donate! :) https://mes.fm/donate 
>
>Reuse of my videos:
>- Feel free to make use of / re-upload / monetize my videos as long as you provide a link to the original video.
>
>Fight back against censorship:
>- Bookmark sites/channels/accounts and check periodically
>- Remember to always archive website pages in case they get deleted/changed.
>
>Join my private Discord chat room: https://mes.fm/chatroom
>
>Check out my Reddit and Voat math forums:
>- Reddit: https://reddit.com/r/AMAZINGMathStuff
>- Voat: https://voat.co/v/AMAZINGMathStuff
>
>Buy "Where Did The Towers Go?" by Dr. Judy Wood: https://mes.fm/judywoodbook
>Follow along my epic video series:
>- #MESScience: https://mes.fm/science-playlist
>- #MESExperiments: https://peakd.com/mesexperiments/@mes/list
>- #AntiGravity: https://peakd.com/antigravity/@mes/series
>-- See Part 6 for my Self Appointed PhD and #MESDuality breakthrough concept!
>- #FreeEnergy: https://mes.fm/freeenergy-playlist
>
>---
>
>NOTE #1: If you don't have time to watch this whole video:
>
>- Skip to the end for Summary and Conclusions (if available)
>- Play this video at a faster speed.
>-- TOP SECRET LIFE HACK: Your brain gets used to faster speed. (#Try2xSpeed)
>-- Try 4X+ speed by browser extensions or modifying source code.
>-- **Browser extension recommendation: https://mes.fm/videospeed-extension**
>-- See my tutorial to learn more: https://peakd.com/video/@mes/play-videos-at-faster-or-slower-speeds-on-any-website
>- Download and read video notes.
>- Read notes on the Hive blockchain #Hive
>- Watch the video in parts.
>
>NOTE #2: If video volume is too low at any part of the video:
>
>- Download this browser extension recommendation: https://mes.fm/volume-extension

---

# Natural Logarithms Defined as Integrals: Introduction

![Natural Log as Integrals Intro.jpeg](https://files.peakd.com/file/peakd-hive/mes/zACQS1WR-Natural20Log20as20Integrals20Intro.jpeg)

Previously logarithmic functions were defined as inverse functions to exponential functions:

![image.png](https://files.peakd.com/file/peakd-hive/mes/RbwoNT9g-image.png)

A better definition is to use the Fundamental Theorem of Calculus and go from there. 

**Definition:** 

The Natural Logarithmic function is defined by:

![image.png](https://files.peakd.com/file/peakd-hive/mes/oYvQbQ4j-image.png)

![image.png](https://files.peakd.com/file/peakd-hive/mes/k5NTGMPC-image.png)

👍 hanshotfirst, steemiteducation, tombstone, punchline, curie, mes, ctime, theregularguy, goblinknackers, techslut, hendrikdegrote, edu-venezuela, edkarnie, sbi6, hanzappedfirst, steemwizards, stayoutoftherz, notb4mycoffee, epicdice, themanny, justtryme90, yangoldberg, karaoke1850, chris4210, matt-a, accelerator, lays, map10k, azizbd, nickyhavey, blueorgy, alvinauh, macoolette, broncofan99, silverwhale, travisung, teacherspet, majes.tytyty, eric-boucher, saboin, furious-one, nerdnews, koskl, curx, bloom, mhm-philippines, dearw, blewitt, blue-pencil, maxuve, yourtop3, freetissues, joshmania, fractalfrank, thecryptosociety, musicvoter, schoolforsdg4, healthexpert, jimshorts, massivevibration, iansart, socialbot, roguewriter, eliel, and 235 others

`author`	mes
`permlink`	natural-logarithms-defined-as-integrals-introduction
`category`	hive-128780
`json_metadata`	{"app":"peakd/2020.03.12","format":"markdown","tags":["mathematics","calculus","science","hiveeducation","steemiteducation","math","education","school","messcience","tutorial"],"users":["mes"],"links":["https://d.tube/#!/v/mes/a77jni9w6uw","https://www.bitchute.com/video/4CKkwspA8RGK/","https://youtu.be/M-N2PQ5UZns","https://1drv.ms/b/s!As32ynv0LoaIg4I9_IzTxQXB9sY_KQ?e=QOOgWk","/@mes","http://mes.fm/subscribe","https://mes.fm/donate","https://mes.fm/chatroom","https://reddit.com/r/AMAZINGMathStuff","https://voat.co/v/AMAZINGMathStuff"],"image":["https://files.peakd.com/file/peakd-hive/mes/zACQS1WR-Natural20Log20as20Integrals20Intro.jpeg","https://files.peakd.com/file/peakd-hive/mes/RbwoNT9g-image.png","https://files.peakd.com/file/peakd-hive/mes/oYvQbQ4j-image.png","https://files.peakd.com/file/peakd-hive/mes/k5NTGMPC-image.png"]}
`created`	2020-03-27 18:06:30
`last_update`	2020-03-27 18:19:48
`depth`	0
`children`	0
`last_payout`	2020-04-03 18:06:30
`cashout_time`	1969-12-31 23:59:59
`total_payout_value`	1.212 HBD
`curator_payout_value`	1.180 HBD
`pending_payout_value`	0.000 HBD
`promoted`	0.000 HBD
`body_length`	3,355
`author_reputation`	296,355,872,989,060
`root_title`	"Natural Logarithms Defined as Integrals: Introduction"
`beneficiaries`	`[]`
`max_accepted_payout`	1,000,000.000 HBD
`percent_hbd`	10,000
`post_id`	96,603,821
`net_rshares`	7,751,707,711,346
`author_curate_reward`	""

properties (23)vote details (299)

voter	rshares	pct
tombstone	509,065,224,271	1.62%
tuck-fheman	655,164,383	4.5%
chris4210	40,258,654,907	4.5%
justtryme90	47,537,376,470	4.5%
eric-boucher	18,396,996,043	4.5%
anwenbaumeister	409,285,126	9%
mammasitta	3,271,086,357	0.45%
matt-a	34,819,594,435	1.5%
diana.catherine	1,036,211,860	4.5%
blueorgy	24,982,799,616	6.75%
kibela	703,090,302	2.7%
eztechwin	3,874,570,841	4.5%
psygambler	793,185,802	4.5%
randomblock1	1,124,758,437	9%
hanshotfirst	2,419,735,391,975	50%
azizbd	25,444,222,577	9%
alaqrab	5,355,419,320	4.5%
lk666	2,987,568,116	4.5%
koskl	15,652,875,059	100%
curie	228,310,475,920	9%
techslut	120,845,111,249	25%
hendrikdegrote	110,115,634,028	9%
bigbear	2,677,114,488	25%
slider2990	4,752,647,931	2.25%
vact	1,497,857,341	9%
giantbear	6,232,567,188	9%
roguewriter	8,950,825,689	4.5%
sweetpea	7,560,540,182	50%
nutman	2,624,145,954	9%
shaunmza	1,793,945,163	4.5%
gmedley	1,929,438,514	4.5%
theregularguy	169,000,064,167	100%
steemiteducation	1,358,007,317,199	90%
decentral	1,105,681,113	2.25%
bloom	14,126,465,108	4.5%
mes	208,026,381,932	100%
arnel	1,964,923,637	4.5%
iansart	9,189,533,623	4.5%
eliel	8,876,299,541	5%
jagged	5,686,066,072	1.8%
bitrocker2020	6,521,433,015	0.45%
improv	4,183,400,297	0.75%
freetissues	10,573,617,160	4.5%
deisip67	1,031,464,011	20%
schoolforsdg4	9,704,466,830	5%
wishmaiden	996,314,343	4.5%
mxzn	5,622,831,006	4.5%
roseri	2,851,844,876	50%
zerotoone	1,820,076,945	4.5%
anacristinasilva	4,179,012,267	5%
locikll	3,308,753,453	18%
aboutyourbiz	1,620,373,837	9%
oscarcede	779,770,452	18%
ghostgtr	1,907,162,196	18%
affiedalfayed	4,177,617,625	36%
furious-one	16,711,812,326	30%
gniksivart	4,334,047,597	2.5%
tngflx	2,105,547,800	2.7%
edkarnie	86,449,963,955	20%
allcapsonezero	4,628,980,864	4.5%
steemwizards	70,069,586,667	100%
neumannsalva	4,504,949,035	4.5%
stayoutoftherz	61,456,440,736	3.6%
ralph-rennoldson	1,488,240,419	1.6%
jimshorts	9,289,096,768	100%
prapanth	1,018,687,663	4.5%
stinawog	788,761,954	5%
dream.trip	523,545,566	9%
guada1	915,632,323	45%
garudi	539,385,257	9%
nerdnews	16,482,138,420	100%
stickchumpion	1,232,781,407	4.5%
olusolaemmanuel	1,704,686,167	6.3%
massivevibration	9,264,848,174	5%
vera-vaders-ea	8,863,461,569	100%
accelerator	29,753,521,083	2.5%
torico	1,619,653,367	2.97%
masterwu	3,078,503,998	27%
estream.studios	535,781,836	5%
yangoldberg	44,004,112,446	9%
karaoke1850	43,503,090,945	100%
minnowpowerup	2,183,993,516	4.5%
majes.tytyty	20,293,494,912	1.8%
dokter-purnama	872,684,277	4.5%
derekvonzarovich	722,253,834	4.5%
cryptononymous	1,133,013,698	4.5%
gotgame	1,751,145,864	4.5%
braveboat	2,452,687,405	8%
jlsplatts	7,360,080,227	1.5%
buttcoins	7,551,903,631	1.8%
gregan	717,748,744	4.5%
divinekids	7,734,917,392	100%
peaceandwar	1,437,327,730	4.5%
tazbaz	860,592,066	4.5%
florian-glechner	2,279,910,011	0.9%
teacherspet	21,036,815,489	100%
battebilly	1,273,920,421	4.5%
notb4mycoffee	51,340,698,945	100%
silverwhale	23,349,122,607	90%
alvinauh	24,913,540,227	30%
lays	25,797,294,596	4.5%
nehomar	643,111,273	9%
sankysanket18	3,303,875,611	4.5%
misterbob	786,476,743	45%
nicole-st	3,489,211,470	4.5%
teukurival	762,084,154	4.5%
drmake	4,990,475,379	4.5%
blue-pencil	12,505,971,283	90%
danile666	5,911,706,546	4.5%
pechichemena	1,801,096,602	1.8%
afifa	834,409,153	10%
mhm-philippines	14,032,880,214	4.5%
hanzappedfirst	71,464,928,352	100%
weirdnews	8,181,255,210	100%
brutledge	602,062,390	4.5%
kenadis	1,051,441,547	4.5%
punchline	246,175,904,951	100%
thescubageek	632,423,847	4.5%
rajib2k5	786,753,024	0.22%
venalbe	1,182,573,822	4.5%
danaedwards	1,066,050,258	9%
dechastre	1,766,939,739	1.8%
phgnomo	674,987,460	4.5%
redcube	4,985,551,465	4.5%
gordon92	973,230,324	4.5%
stahlberg	2,085,754,029	4.5%
gabrielatravels	2,044,431,206	4.5%
reizak	828,042,367	3.6%
carn	836,035,230	6.75%
iamjadeline	2,525,813,939	1.35%
saintchristopher	2,665,709,752	9%
soufianechakrouf	2,011,640,927	2.7%
shinedojo	1,012,777,841	9%
bennettitalia	1,546,801,745	2.25%
steveblucher	5,092,550,958	45%
curx	14,583,594,381	5%
womenempowerment	2,284,139,221	5%
steemboat-steve	907,946,239	4.5%
kylo-ren	7,624,794,653	100%
mashiliyanage	1,302,958,689	45%
rachaeldwatson	659,588,719	4.5%
didic	4,025,817,210	4.5%
operahoser	843,927,676	1.35%
upfundme	556,602,323	0.45%
raise-me-up	0	0.01%
sandracabrera	2,483,777,148	45%
oghie	955,676,711	50%
ejlo3310	2,470,533,584	45%
vegan.niinja	583,130,311	4.5%
cyprianj	1,142,490,206	9%
bernardino	545,855,233	4.5%
forester-joe	704,809,996	1.5%
zipporah	4,471,647,837	1.8%
ambitiouslife	548,270,751	4.5%
positiveninja	1,127,862,244	4.5%
deathlyhorror	3,255,535,693	4.5%
steemlibs	678,489,441	4.5%
foxyspirit	1,284,715,036	4.5%
lordjames	8,191,870,634	4.5%
bscrypto	4,508,785,667	2.25%
movingman	5,911,660,003	5%
bil.prag	932,103,540	0.45%
camiloferrua	4,246,580,977	4.95%
sanderjansenart	4,046,303,366	4.5%
vittoriozuccala	2,320,209,829	4.5%
qberry	4,631,855,653	4.5%
broncofan99	23,552,418,765	20%
rambutan.art	2,024,111,935	9%
alanasteemit	744,516,550	45%
genoner	564,623,467	8.55%
c0wtschpotato	786,783,465	4.5%
misan	739,650,729	4.5%
misia1979	900,700,195	4.5%
dearw	13,005,757,925	9%
outtheshellvlog	1,151,468,394	4.5%
saboin	17,459,350,580	2.25%
srijana-gurung	2,030,994,843	4.5%
apteacher	2,203,283,231	18%
musicvoter	9,779,529,048	2%
nickyhavey	25,125,270,855	4.5%
aceaeterna	4,342,421,578	45%
ojap02	905,194,795	90%
steemjet	1,036,003,970	4.5%
motherofalegend	907,495,237	4.5%
musicvoter2	8,365,606,252	1%
myfreebtc	6,358,853,167	6.3%
drawmeaship	584,270,259	4.5%
schroders	3,569,925,337	2.7%
hardaeborla	541,133,672	4.5%
cheese4ead	1,500,290,752	4.5%
blewitt	12,756,068,356	0.45%
sbi6	76,423,432,013	99.65%
fernando.lubezki	615,210,903	8.1%
ilovecryptopl	1,346,154,623	7.2%
bflanagin	5,702,478,876	4.5%
lillywilton	1,387,361,144	20%
call-me-howie	843,979,973	4.5%
gerdtrudroepke	1,357,035,486	2.25%
hansmast	683,535,943	4.5%
goblinknackers	121,999,027,780	4%
jk6276	1,928,768,646	2.7%
dronegraphica	686,658,741	2.25%
kylealex	5,219,970,359	10%
arnilarn	610,366,870	9%
themanny	48,757,009,413	100%
minimining	1,023,458,726	4.5%
edu-venezuela	106,122,819,647	100%
supersoldier	3,944,855,989	100%
donkeyslayer	3,942,538,559	100%
fulltimebot1	4,230,249,605	100%
fulltimebot2	4,145,073,924	100%
fulltimebot3	4,636,017,472	100%
fulltimebot7	4,538,959,013	100%
fulltimebot9	4,474,354,960	100%
fulltimebot10	4,522,050,165	100%
hanshotfirst-sm	7,799,086,790	100%
bigpun	558,621,273	100%
justperfect	1,597,860,015	100%
townmayor	1,511,454,017	100%
annaabi	1,066,233,275	4.5%
marcocasario	8,445,938,432	4.5%
trang	845,264,822	4.5%
fulltimebot15	4,341,935,717	100%
fulltimebot16	4,297,316,643	100%
fulltimebot17	4,072,829,899	100%
fulltimebot21	4,265,175,944	100%
fulltimebot24	4,220,752,477	100%
fulltimebot28	4,177,844,632	100%
fulltimebot29	4,369,362,591	100%
fulltimebot33	4,158,381,574	100%
fulltimebot36	4,288,255,425	100%
fulltimebot37	4,171,275,346	100%
fulltimebot40	4,089,976,525	100%
fulltimebot42	4,074,240,334	100%
fulltimebot43	4,152,760,310	100%
fulltimebot47	4,160,870,996	100%
fulltimebot48	4,111,576,205	100%
fulltimebot50	4,164,780,357	100%
fulltimebot51	4,004,473,490	100%
fulltimebot53	4,199,920,443	100%
fulltimebot58	4,356,041,649	100%
fulltimebot59	4,411,879,003	100%
fulltimebot60	4,231,619,403	100%
palasatenea	775,066,769	4.5%
knightbjj	1,424,472,904	6.75%
the.success.club	3,862,459,408	4.5%
chickenmeat	1,858,964,593	4.5%
macoolette	24,057,044,826	1.8%
javier.dejuan	1,993,547,504	9%
tommyl33	1,150,719,832	4.5%
fulltimebot66	4,085,288,681	100%
fulltimebot69	4,139,475,544	100%
fulltimebot71	3,635,952,621	100%
fulltimebot74	3,792,365,639	100%
a-non-e-moose	703,033,623	100%
reverseacid	683,167,277	4.5%
pushpedal	883,813,653	4.5%
deepsouthpiddlin	3,380,993,189	20%
alvin0617	811,708,966	4.5%
solarphasing	690,867,294	5%
ecodesigns	4,846,636,282	45%
khan.dayyanz	1,712,614,352	9%
ppss	612,709,353	8.82%
healthexpert	9,398,092,127	4.5%
vaultec	3,850,855,559	12%
steemegg	851,237,925	2.25%
travisung	22,459,517,656	4.5%
loliver	906,852,484	4.5%
ctime	186,482,941,708	2%
rem-steem	2,689,439,927	1.8%
pulleyhead	2,146,857,643	9%
cecilian	537,402,462	4.5%
bluemaskman	804,426,819	4.5%
hashkings	1,900,309,402	0.9%
breakout101	1,051,480,282	4.5%
the.curator	628,887,595	5%
filosof103	1,314,772,434	4.5%
begood2me	1,052,495,625	4.5%
epicdice	50,626,226,612	2.7%
socialbot	8,970,463,354	5%
fractalfrank	10,254,203,075	4.5%
ph1102	8,233,698,176	8.1%
titan-c	2,810,868,758	9%
map10k	25,772,655,452	10%
shimozurdo	718,847,726	4.5%
onecent	2,445,123,986	70%
mapxv	6,991,005,581	2.5%
drlobes	717,452,601	4.5%
ufm.pay	2,308,153,426	0.33%
maxuvd	1,662,772,124	2.5%
maxuve	11,278,518,409	2.5%
steem.consultant	1,136,425,992	1.8%
andylein	3,642,070,235	4.5%
joshmania	10,331,620,506	4.5%
yourtop3	10,836,137,202	3.6%
stemisaria	1,922,731,587	100%
roamingsparrow	1,964,635,326	6.75%
traveler-hwi	2,064,003,518	4.5%
thecryptosociety	9,949,260,003	25%