Mathematics: What is 4log 1/2w+(2log 1/2u-3log 1/2v) written as a single logarithm

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What is 4log 1/2w+(2log 1/2u-3log 1/2v) written

salvadorperez26

12.03.2022

The given expression is

$4log_{1/2}w+(2 log_{1/2}u-3log_{1/2}v)$

First we use the following rule

$a \ log_{b} c = log _{b} c^a$

And on using this rule, we will get

$log_{1/2} w^4 + ( log_{1/2}u^2-log_{1/2}v^3 )$

Now we use the following two rules

$log a + log b = log(ab)
\\
log a- log b =log( \frac{a}{b} )$

And on using these two rules, we will get

$=log_{1/2}w^4 + log_{1/2} ( \frac{u^2}{v^3})
\\
= log_{1/2} (\frac{ w^4 u^2}{v^3} )$

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