Question

need help with ln e^4

Answer 1

\[x=\ln e ^{4}\]\[e ^{x}=e ^{4}\]\[x =4\]

Answer 2

how do they get from
\[x =\ln e ^{4}\]
to
\[e ^{x}=e ^{4}\]
sorry if its dumb question.
I am aware that
\[\ln e ^{4}=\log_{e}e ^{4} =4\]
I am just wondering about the algebra used here.

Answer 3

they could have skipped the second step and immediately get x=4. but what they did was they took exponential of both sides which resulted in that second line

Answer 4

what do u mean exponential of both sides

Answer 5

wait.. cause x = ln x ?

Answer 6

no.
\[x=\ln \exp(4)\]
\[\exp(x)=\exp \ln \exp(4)\]
so
\[\exp(x)=\exp(x)\]

Answer 7

**\[\exp(x)=\exp(4)\]

Answer 8

\[e ^{x}=e ^{\ln e ^{4}}\]

Answer 9

?

Answer 10

yea

Answer 11

what is the rule that allows you to drop the ln from the right side exponent?

Answer 12

exp and ln are inverse functions of each other so exp and ln cancel each other

Answer 13

wooo awesome.. thats what i am missing in my head. so u dont see ln in exponentials ;p

Answer 14

thanks for sticking with me.. my brain gets so stuck on easy stuff... i just feel like i need to know every possible way