Question

Which expression is equivalent to log Subscript 12 Baseline (StartFraction one-half Over 8 w EndFraction?

Answer 1

The options are:

$(A)log_{12}8-log_{12}\frac{1}{2}+log_{12}w\\(B)log_{12}\frac{1}{2}-(log_{12}8+log_{12}w)\\(C)log_{12}\frac{1}{2}-log_{12}8+log_{12}w\\(D)\frac{log_{12}\frac{1}{2}}{log_{12}8}+log_{12}w$

Answer:

$[B] log_{12}\frac{1}{2}- (log_{12}8+ log_{12}w).$

Step-by-step explanation:

Given the expression:

$log_{12}\dfrac{\frac{1}{2}}{8w}$

Step 1: Apply the division law of logarithm

$log_{x}\dfrac{a}{b}= log_x}a- log_{x}b$

Therefore:

$log_{12}\dfrac{\frac{1}{2}}{8w}= log_{12}\frac{1}{2}- log_{12}{8w}$

STEP 2:Apply the multiplication law of logarithm.

$log_{x}ab= log_{x}a+ log_{x}b$

Therefore:

$log_{12}{8w}= log_{12}8+ log_{12}w$

STEP 3: Substitute the result from step 2 into the result from step 1

$log_{12}\dfrac{\frac{1}{2}}{8w}= log_{12}\frac{1}{2}- (log_{12}8+ log_{12}w).$

The correct option is B.