Respuesta :
Given:
The expression is:
[tex]4\log_{\frac{1}{2}}w+(2\log_{\frac{1}{2}}u-3\log_{\frac{1}{2}}v)[/tex]
To find:
The single logarithm for the given expression.
Solution:
We have,
[tex]4\log_{\frac{1}{2}}w+(2\log_{\frac{1}{2}}u-3\log_{\frac{1}{2}}v)[/tex]
It can be written as:
[tex]=\log_{\frac{1}{2}}w^4+(\log_{\frac{1}{2}}u^2-\log_{\frac{1}{2}}v^3)[/tex] [tex][\because \log a^b=b\log a][/tex]
[tex]=\log_{\frac{1}{2}}w^4+\log_{\frac{1}{2}}\dfrac{u^2}{v^3}[/tex] [tex][\because \log \dfrac{a}{b}=\log a-\log b][/tex]
[tex]=\log_{\frac{1}{2}}\left(w^4\times \dfrac{u^2}{v^3}\right)[/tex] [tex][\because \log ab=\log a+\log b][/tex]
[tex]=\log_{\frac{1}{2}}\dfrac{w^4u^2}{v^3}[/tex]
Therefore, the correct option is B.
