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

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Answer 1 · 2016-03-14T01:21:11

$x = 0$

$If log_n x = a$ 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 $x = 0$

How do you evaluate log_10(log_2[log_3 9])= xlog_10(log_2[log_3 9])= x?