Question

How are e and ln related? If I have e^(4x) and x=ln2, where can I go from there? (This is calc related)

Answer 1

f(x) = e^x and g(x) = ln(x) are inverse functions of each other:

\[ f(g(x)) = e^{\ln x} = x\]
\[ g(f(x)) = \ln(e^x) = x \]

Answer 2

Therefore, if \( x = \ln 2 \), then
\[ 4x = 4 \ln 2 = \ln(2^4) = \ln(16) \]
and hence
\[ e^{4x} = ... what? \]

Answer 3

It's equal to 16, then?

Answer 4

Yes

Answer 5

Awesome! Thanks!