Question

value of log 2 ( log 5 625) is

Answer 1

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Answer 2

The value of $\log_2 (\log_5 625)=2$.

Step-by-step explanation:

We have,

$\log_2 (\log_5 625)$

To find, the value of $\log_2 (\log_5 625)=?$

∴ $\log_2 (\log_5 625)$

$=\log_2 (\log_5 5^{4} )$

$=\log_2 (4\log_5 5)$

[ ∵ $\log a^{m}=m\log a$]

$=\log_2 (4\times 1)$

[ ∵$\log_a a=1$]

$=\log_2 2^{2}$

$=2\log_2 2$

$=2\times 1=2$

Hence, the value of $\log_2 (\log_5 625)=2$.