How do I solve $log_0.25[ (log_2 3)(log_3 4)]$ ?

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Answer 1 · 2017-10-14T16:02:12

The answer is $-1/2$ .

Start by rewrite $0.25$ as $1/4$ .

$=log_(1/4)[(log_2 3)(log_3 4)]$

We can now use the change of base formula, which states that $log_a n =logn/loga$ .

$=log_(1/4) [ (log3)/(log2) * log4/log3]$

$=log_(1/4) (log4/log2)$

$=log_(1/4) (log(2^2)/log2)$

$=log_(1/4) ((2log2)/log2)$

$=log_(1/4) 2$

Once again we use the change of base formula.

$=log2/(log(1/4)$

$=log2/(log2^-2)$

$=log2/(-2log2)$

$=-1/2$

Hopefully this helps!

How do I solve log_0.25[ (log_2 3)(log_3 4)]log_0.25[ (log_2 3)(log_3 4)] ?