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

Option D is correct.

`\log_4 8 - 2 \log_4 x` is the expression which is equivalent to
`\log_4 (8)/(x^2)`

Explanation:

Given the expression:
`\log_4 (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 (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 (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`