The given expression is
[tex]4log_{1/2}w+(2 log_{1/2}u-3log_{1/2}v)[/tex]
First we use the following rule
[tex]a \ log_{b} c = log _{b} c^a[/tex]
And on using this rule, we will get
[tex]log_{1/2} w^4 + ( log_{1/2}u^2-log_{1/2}v^3 )[/tex]
Now we use the following two rules
[tex]log a + log b = log(ab)
\\
log a- log b =log( \frac{a}{b} )[/tex]
And on using these two rules, we will get
[tex]=log_{1/2}w^4 + log_{1/2} ( \frac{u^2}{v^3})
\\
= log_{1/2} (\frac{ w^4 u^2}{v^3} )[/tex]
