Question

What is the value of log5^{125}?

Answer 1

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.