Question

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

Answer 1

Answer:

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

Step-by-step explanation:

Given

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

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:

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

To further simplify:

$\log(\frac{a}{b}) = \log(a) - \log(b)$

So, we have:

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

Open brackets

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