How do I solve ${log}_{0.25} [({log}_{2} 3) ({log}_{3} 4)]$ $log_0.25[ (log_2 3)(log_3 4)]$ ?

Question

How do I solve ${log}_{0.25} [({log}_{2} 3) ({log}_{3} 4)]$ $log_0.25[ (log_2 3)(log_3 4)]$ ?

1 Answer

Impact of this question

2259 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-10-14T16:02:12

The answer is $- \frac{1}{2}$ $-1/2$ .

Explanation:

Start by rewrite $0.25$ $0.25$ as $\frac{1}{4}$ $1/4$ .

$= {log}_{\frac{1}{4}} [({log}_{2} 3) ({log}_{3} 4)]$ $=log_(1/4)[(log_2 3)(log_3 4)]$

We can now use the change of base formula, which states that ${log}_{a} n = \frac{log n}{log a}$ $log_a n =logn/loga$ .

$= {log}_{\frac{1}{4}} [\frac{log 3}{log 2} \cdot \frac{log 4}{log 3}]$ $=log_(1/4) [ (log3)/(log2) * log4/log3]$

$= {log}_{\frac{1}{4}} (\frac{log 4}{log 2})$ $=log_(1/4) (log4/log2)$

$= {log}_{\frac{1}{4}} (\frac{log (2^{2})}{log 2})$ $=log_(1/4) (log(2^2)/log2)$

$= {log}_{\frac{1}{4}} (\frac{2 log 2}{log 2})$ $=log_(1/4) ((2log2)/log2)$

$= {log}_{\frac{1}{4}} 2$ $=log_(1/4) 2$

Once again we use the change of base formula.

$= \frac{log 2}{log (\frac{1}{4})}$ $=log2/(log(1/4)$

$= \frac{log 2}{{log 2}^{- 2}}$ $=log2/(log2^-2)$

$= \frac{log 2}{- 2 log 2}$ $=log2/(-2log2)$

$= - \frac{1}{2}$ $=-1/2$

Hopefully this helps!

Science

Math

Humanities

... and beyond

How do I solve ${log}_{0.25} [({log}_{2} 3) ({log}_{3} 4)]$ $log_0.25[ (log_2 3)(log_3 4)]$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do I solve log_0.25[ (log_2 3)(log_3 4)]log0.25[(log23)(log34)]log_0.25[ (log_2 3)(log_3 4)] ?

1 Answer

Explanation:

Related questions

Impact of this question

How do I solve ${log}_{0.25} [({log}_{2} 3) ({log}_{3} 4)]$ $log_0.25[ (log_2 3)(log_3 4)]$ ?