## wcaprar How are e and ln related? If I have e^(4x) and x=ln2, where can I go from there? (This is calc related) 2 years ago 2 years ago

1. JamesJ

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

2. JamesJ

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

3. wcaprar

It's equal to 16, then?

4. JamesJ

Yes

5. wcaprar

Awesome! Thanks!