Question

Express 45 = x as a logarithmic equation.

Answer 1

`4^5=x` as a logarithmic equation
`\log_4 (x)=5`

Explanation:

Given : Expression
`4^5=x`

To find : Express the expression as a logarithmic equation?

Solution :

Expression
`4^5=x`

Taking log with base 4 both side,

`\log_4(4^5)=\log_4 (x)`

Using logarithmic property,
`\log_a a^b=b`

`5=\log_4 (x)`

Therefore,
`4^5=x` as a logarithmic equation
`\log_4 (x)=5`

Answer 2

`5 = log_(4)x`

Explanation:

You know that
`45=4^(5)`

Then:
`4^(5)=x`

Taking log with base 4 in both sides, we have:

`log_(4) 4^(5)=log_(4)x`

Applying the logarithmic rules, we have:

`log_(4)4^(5)=log_(4)x` →
`5log_(4)4=log_(4)x`

→
`5 = log_(4)x`

In conclusion, 45 = x expressed as a logarithmic equation equals:
`5 = log_(4)x`