# Math Help - log. problems

1. ## log. problems

a) log9 1/81= x

b) logx81=4

2. #1 has something missing.

#2) $\log_{x}81=4$

Thus $x^4=81$

I don't know exactly what method your teacher wants you to solve these, but this one works out nicely as 3.

3. Hello, robinpatrick!

Rewrite in exponential form . . .

$a)\;\log_9\left(\frac{1}{81}\right) \:=\:x$

We have: . $9^x\:=\:\frac{1}{81} \:=\:\frac{1}{9^2}$

Then: . $9^x\:=\:9^{-2}\quad\Rightarrow\quad x = -2$

$b)\;\log_x(81)\:=\:4$

We have: . $x^4\:=\:81$

Then: . $x^4\:=\:3^4\quad\Rightarrow\quad x = 3$