2 Answers

Sodium · Answer 1 · 2022-10-16T10:55:03+0000

Answer:

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

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

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

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