Question

What is 4 log Subscript one-half Baseline w + (2 log Subscript one-half Baseline u minus 3 log Subscript one-half Baseline v) written as a single logarithm?
4 log Subscript one-half Baseline 2 Superscript 4 Baseline u squared minus v cubed
log Subscript one-half Baseline w Superscript 4 Baseline (StartFraction u squared Over v cubed EndFraction)
log Subscript one-half Baseline (StartFraction w Superscript 4 Baseline Over u squared v cubed EndFraction)
log Subscript one-half Baseline (w (StartFraction u squared Over v cubed EndFraction)) Superscript 4

Answer 1

Given:

The expression is:

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

To find:

The single logarithm for the given expression.

Solution:

We have,

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

It can be written as:

$=\log_{\frac{1}{2}}w^4+(\log_{\frac{1}{2}}u^2-\log_{\frac{1}{2}}v^3)$       $[\because \log a^b=b\log a]$

$=\log_{\frac{1}{2}}w^4+\log_{\frac{1}{2}}\dfrac{u^2}{v^3}$       $[\because \log \dfrac{a}{b}=\log a-\log b]$

$=\log_{\frac{1}{2}}\left(w^4\times \dfrac{u^2}{v^3}\right)$      $[\because \log ab=\log a+\log b]$

$=\log_{\frac{1}{2}}\dfrac{w^4u^2}{v^3}$

Therefore, the correct option is B.