Question

ln e^x = -4

Answer 1

A rule of logs tells us:\[\Large\rm \log(a^{\color{orangered}{b}})=\color{orangered}{b}\log(a)\]

Answer 2

Do you understand how we can apply this rule to our problem?
\[\Large\rm \ln(e^{\color{orangered}{x}})=-4\]

Answer 3

Okay, I think so, gimme a minute, thank you

Answer 4

xlog(e)

Answer 5

Ok great.
From there, we should remember something else important about logs.

Answer 6

Alright.

Answer 7

Whenever the `base` matches the `contents` of the log, the result is 1.

Some examples:\[\Large\rm \log_2(2)=1\]\[\Large\rm \log_{10}(10)=1\]

Answer 8

We can think of the natural log like this:\[\Large\rm \ln(e)=\log_e(e)\]

Answer 9

\[\Large\rm \ln(e^{\color{orangered}{x}})=-4\]\[\Large\rm \color{orangered}{x}\log_e(e)=-4\]

Answer 10

Hmm so what can we do with that information?

Answer 11

since we have xlog(e),
ln(e^x) = -4
-4?

Answer 12

I'm not exactly sure what you meant by that >.<
But yes, our x value will end up being -4.

\[\Large\rm \color{orangered}{x}\log_e(e)=-4\]\[\Large\rm \color{orangered}{x}\cancel{\log_e(e)}1=-4\]\[\Large\rm \color{orangered}{x}=-4\]

Answer 13

Oh, haha yeah I'm not too good with this lesson, but I understand it enough to get past it for now. Thank you so much I will look back to this whenever I have a problem :D