Question

HHHEEEELLLPPPP INVERSES f(x)e^2x

Answer 1

@jdoe0001

Answer 2

hmm have you covered logarithms yet?

Answer 3

I assume is \(\large \bf f(x)=e^{2x}\)

you'd end up with a logarithmic function though, thus... have you covered logarithms yet?

Answer 4

would you take the natural log?

Answer 5

and yes

Answer 6

\[\frac{ x }{ e^2 }\]

Answer 7

Maybe?

Answer 8

\[\ln x =\ln e ^{2y}\]

Answer 9

then move the 2y in front?

Answer 10

ok.... so...
let us use the log cancellation rule of .

actually... yes... let us use the exponent instead

Answer 11

and In e = 1
so it would be...\[\ln x=2y\]

Answer 12

oh okay

Answer 13

\(\bf f(x)=y=e^{2x}\qquad inverse\implies x=e^{2y}
\\ \quad \\
log_{\color{brown}{ e}}x=log_{\color{brown}{ e}}({\color{brown}{ e}}^{2y})\implies log_e(x)=2y{\color{purple}{ log_e(e)}}\implies ln(x)=2y\cdot {\color{purple}{ 1}}
\\ \quad \\
\cfrac{ln(x)}{2}=y\)