Question

Alg 2 help

Answer 1

@ahamed. @ghuczek @hartnn

Answer 2

I will try to help

Answer 3

Yea he will try to help ._.
pretend im not here again ._.

Answer 4

Inverse function of an exponential function
okay, lets tackle it in general:

\(\LARGE\color{black}{ \displaystyle \color{red}{f(x)}= {\rm \color{blue}{a}}({\rm \color{green}{b}})^{\color{brown}{x}} }\)

\(\scriptsize\color{ slate }{\scriptsize{\bbox[5pt, royalblue ,border:2px solid royalblue ]{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ }}}\)

Where,
\(\LARGE\color{black}{ \displaystyle \left\{ {\rm \color{green}{b}}:{\rm \color{green}{b}}>0 ,~~{\rm \color{green}{b}}\ne 1\right\}}\)
\(\LARGE\color{black}{ \displaystyle \left\{ {\rm \color{blue}{a}}:{\rm \color{blue}{a}}\ne0 \right\}}\)
and of course, we are taking when
\(\LARGE\color{black}{ \displaystyle \left\{ {\rm \color{blue}{a}},~~{\rm \color{green}{b}},~~\color{brown}{x},~~\color{red}{y}\right\}~\in~{\bf R}}\)

\(\scriptsize\color{ slate }{\scriptsize{\bbox[5pt, royalblue ,border:2px solid royalblue ]{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ }}}\)

\(\LARGE\color{black}{ \displaystyle \color{red}{y}= {\rm \color{blue}{a}}({\rm \color{green}{b}})^{\color{brown}{x}} }\)


replacing the \(\large \color{black}{ \displaystyle \color{red}{y} }\) and \(\large \color{black}{ \displaystyle \color{brown}{x} }\)


\(\LARGE\color{black}{ \displaystyle \color{brown}{x}= {\rm \color{blue}{a}}({\rm \color{green}{b}})^{\color{red}{y}} }\)


\(\LARGE\color{black}{ \displaystyle \frac{\color{brown}{x}}{{\rm \color{blue}{a}}}= ({\rm \color{green}{b}})^{\color{red}{y}} }\)


\(\LARGE\color{black}{ \displaystyle {\rm Log}_{{\tiny~~} \color{green}{b}} \left(\frac{\color{brown}{x}}{{\rm \color{blue}{a}}} \right)= {\rm Log}_{{\tiny~~} \color{green}{b}} ({\rm \color{green}{b}})^{\color{red}{y}} }\)


\(\LARGE\color{black}{ \displaystyle {\rm Log}_{{\tiny~~} \color{green}{b}} \left(\frac{\color{brown}{x}}{{\rm \color{blue}{a}}} \right)= {\color{red}{y}}{\tiny~~~}{\rm Log}_{{\tiny~~} \color{green}{b}} ({\rm \color{green}{b}}) }\)


\(\LARGE\color{black}{ \displaystyle {\rm Log}_{{\tiny~~} \color{green}{b}} \left(\frac{\color{brown}{x}}{{\rm \color{blue}{a}}} \right)= {\color{red}{y}} }\)


\(\LARGE\color{black}{ \displaystyle{\color{red}{f^{-1}(x)}}= {\rm Log}_{{\tiny~~} \color{green}{b}} \left(\frac{\color{brown}{x}}{{\rm \color{blue}{a}}} \right) }\)

Answer 5

finally got to post this... sorry it took long... I disconnected twice while posting

Answer 6

you can expand it, but this is how it is...