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

The answer is B :))

Explanation:

Answer 2

Given:

The expression is:

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

To find:

The single logarithm for the given expression.

Solution:

We have,

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

It can be written as:

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

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

`=\log_{(1)/(2)}\left(w^4* (u^2)/(v^3)\right)`
`[\because \log ab=\log a+\log b]`

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

Therefore, the correct option is B.