a) log9 1/81= x
b) logx81=4
Hello, robinpatrick!
Rewrite in exponential form . . .
$\displaystyle a)\;\log_9\left(\frac{1}{81}\right) \:=\:x$
We have: .$\displaystyle 9^x\:=\:\frac{1}{81} \:=\:\frac{1}{9^2}$
Then: .$\displaystyle 9^x\:=\:9^{-2}\quad\Rightarrow\quad x = -2$
$\displaystyle b)\;\log_x(81)\:=\:4$
We have: .$\displaystyle x^4\:=\:81$
Then: .$\displaystyle x^4\:=\:3^4\quad\Rightarrow\quad x = 3$