Question

Which of the following expressions is equivalent to the logarithmic expression below? log 4 (8/x^2) A. log 4 8 + 2 log 4 x B. 2 log 4 8 - log 4 x C. 2 log 4 8 + log 4 x D. log 4 8 - 2 log 4 x

Answer 1

log 4 8/x² = log 4 8 - log 4 x² =

log 4 8 - 2log 4 x

correct choice is D

Answer 2

Answer:

Option D is correct.

$\log_4 8 - 2 \log_4 x$ is the expression which is equivalent to  $\log_4 \frac{8}{x^2}$

Step-by-step explanation:

Given the expression:  $\log_4 \frac{8}{x^2}$          ......[1]

The notation of a logarithm is derived from exponents, all logarithmic rules for multiplication, division and raised to a power are based on those for exponents.

Using logarithmic rule:

$\log_b \frac{x}{y} = \log_b x - \log_b y$ ; b is the base

$\log_b x^n = n \log_b x$

By using logarithmic rule;

[1] ⇒  $\log_4 \frac{8}{x^2}= \log_4 8 - \log_4 x^2$

=$\log_4 8 - 2 \log_4 x$  

Therefore, the following expression is equivalent to the given logarithmic expression is; $\log_4 8 - 2 \log_4 x$