1. ## Logarithm as inverse

Write the inverse of each function.

Please show work and short explanation so I understand how to get the answers for the rest of my homework

1) $\displaystyle Y=2^{x/3}$

2) $\displaystyle Y=log_{5} X^2$

Also If I Need to solve for Y in the following what is the answer for the following (please show work):

$\displaystyle f(x)=log_4(x+4)-3$
$\displaystyle X= -2$

2. Originally Posted by north1224
Also If I Need to solve for Y in the following what is the answer for the following (please show work):

$\displaystyle f(x)=log_4(x+4)-3$
$\displaystyle X= -2$

well lets say you have $\displaystyle log_{base} number$. This is equivalent to $\displaystyle log_{x} number / log_{x} base$ with x being whatever you want.....10 for calculating purposes

so

$\displaystyle f(x)=log_4(x+4)-3$
$\displaystyle x =2$

$\displaystyle f(x)=log_4(2+4)-3$
$\displaystyle f(x)=log_4(6) -3$
$\displaystyle f(x)=(log_{10}(6) / log_{10}(4) ) -3$
$\displaystyle f(x)=~1.2925 - 3 = -1.7075$