Question

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

Answer 1

C.

Step-by-step explanation:

Edge 2021

Answer 2

`\log_5((x)/(4))^2 = 2\log_5(x) - 2\log_5(4)`

Step-by-step explanation:

Given

`\log_5((x)/(4))^2`

Required

The equivalent expression

To do this, we apply the following law of indices:

`\log_a(b)^c = c\log_a(b)`

So, we have:

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

To further simplify:

`\log((a)/(b)) = \log(a) - \log(b)`

So, we have:

`\log_5((x)/(4))^2 = 2(\log_5(x) - \log_5(4))`

Open brackets

`\log_5((x)/(4))^2 = 2\log_5(x) - 2\log_5(4)`