Question

Find the Inverse of f(x)= log(base 2) x-3

Answer 1

I assume you've covered logarithms by now?

Answer 2

Yes

Answer 3

well if you recall to find the "inverse relation" we simply swap about the variables, that is \(\bf f(x)={\color{brown}{ y}}=log_2({\color{blue}{ x}}-3)\qquad inverse\implies {\color{blue}{ x}}=log_2({\color{brown}{ y}}-3)\)

then we just solve for "y"

any ideas?

Answer 4

Not sure

Answer 5

\(\bf f(x)={\color{brown}{ y}}=log_2({\color{blue}{ x}}-3)\qquad inverse\implies {\color{blue}{ x}}=log_2({\color{brown}{ y}}-3)
\\ \quad \\
\textit{log cancellation rule of }\large {\color{red}{ a}}^{log_{\color{red}{ a}}x}=x\qquad thus
\\ \quad \\
x=log_2(y-3)\implies{ \large {\color{red}{ 2}}^x={\color{red}{ 2}}^{log_{\color{red}{ 2}}(y-3)}}\implies 2^x=y-3
\\ \quad \\
2^x+3=y \iff f^{-1}(x)\)

Answer 6

Ok, so the inverse is solving for Y?

Answer 7

Thanks!

Answer 8

well..yes

Answer 9

yw