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((8)/(x^2))`

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

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

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

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

which corresponds to option B