Question

Which of the following expressions is equivalent to the logarithmic expression below?A.2 log4 8 + log4 xB.log4 8 - 2 log4 xC.2 log4 8 - log4 xD.log4 8 + 2 log4 x

Answer 1

We are given the logarithm

$log_4(\frac{8}{x^2})$

Recall that given positive numbers a and b, a property of logarithms is

$log_c(\frac{a}{b})=log_c(a)\text{ -log\_c\lparen b\rparen}^$

so if we applyt this property to our situation, we get

$log_4(\frac{8}{x^2})=log_4(8)\text{ -log\_4\lparen x}^2)$

now, we use another property from logarithms, which is: Given numbers a and b, we have that

$log_c(a^b)=b\cdot log_c(a)$

so, if we apply this property to the second logarithm we get

$log_4(x^2)=2\cdot log_4(x)$

so our final answer is

$log_4(\frac{8}{x^2})=log_4(8)\text{ -2log\_4\lparen x\rparen}$

which corresponds to option B