Question

Which expression is equivalent to log Subscript 5 Baseline (StartFraction x Over 4 EndFraction) squared?

Answer 1

The answer is c

Explanation:

Answer 2

`2\,log_5(x)-2\,log_5(4)` which is the third listed option

Explanation:

We use the properties of logarithms, starting with the property for exponents (
`log_b(a^n)=n\,*\,log_b(a)`), so we get:

`log_5((x)/(4) )^2=2\,*\,log_5((x)/(4) )`

and now we use the property of log of a quotient (
`log_b((x)/(y) )=log_b(x)-log_b(y)`), which continuing with our case gives:

`2\,*\,log_5((x)/(4) )= 2\,*[log_5(x)-log_5(4)]=2\,log_5(x)-2\,log_5(4)`

This coincides with the third option listed among the possible answers