1 Answer

Arun Kumar P · Answer 1 · 2021-03-05T12:04:49+0000

The value of
$\log_5{125}$ is 3.

Solution:

Step 1: Given expression is
$log_5{125}$ .

125 can be expressed as
5^3.

$\log_5{125}=\log_5{5}^3$

Step 2: Using log rule:
$\log_a{x^b}=b\log_a{x}$

$\log_5{5}^3=3\log_5{5}$

Step 3: Using log rule:
$\log_a{a}=1$

$\log_5{5}= 1$

⇒
$3\log_5{5}= 3(1)$

⇒
$3\log_5{5}= 3$

∴
$\log_5{125}=3$

Hence the value of
$\log_5{125}$ is 3.

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