# How do you evaluate log_10(log_2[log_3 9])= x?

Mar 14, 2016

$x = 0$

#### Explanation:

$I f {\log}_{n} x = a$ Then $x = {n}^{a}$

In the question x is equal to a nest of log functions of different bases as follows:

$a = {\log}_{3} 9$
$b = {\log}_{2} a$
$x = {\log}_{10} b$

Taking each in turn:

$a = {\log}_{3} 9 = 2$ Since $9 = {3}^{2}$
$b = {\log}_{2} 2 = 1$ Since $2 = {2}^{1}$
$x = {\log}_{10} 1 = 0$ Since $1 = {10}^{0}$

Hence $x = 0$