Question

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

Answer 1

Answer:

The answer is c

Step-by-step explanation:

Answer 2

Answer:

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

Step-by-step explanation:

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

$log_5(\frac{x}{4} )^2=2\,*\,log_5(\frac{x}{4} )$

and now we use the property of log of a quotient ($log_b(\frac{x}{y} )=log_b(x)-log_b(y)$), which continuing with our case gives:

$2\,*\,log_5(\frac{x}{4} )= 2\,*[log_5(x)-log_5(4)]=2\,log_5(x)-2\,log_5(4)$

This coincides with the third option listed among the possible answers