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.