## Task A-3.1. (4 points)

If $\log _{a} x=3$ and $\log _{a b} x=2$, what is $\log _{b} x$?
## Second solution.

Obviously $x \neq 1$, so from $\log _{a} x=3$ it follows that $\log _{x} a=\frac{1}{3}$,

and from $\log _{a b} x=2$ it follows that $\log _{x} a b=\frac{1}{2}$.

Since $\log _{x} a b=\log _{x} a+\log _{x} b$, it follows that $\frac{1}{3}+\log _{x} b=\frac{1}{2}$,

so $\log _{x} b=\frac{1}{6}$ and finally $\log _{b} x=6$.