Question

Evaluate the following by converting into exponential form:

log₅ 0.04

Answer 1

Given: log₅ 0.04

Step-wise calculation:

1. Let log₅ 0.04 = x, so 5^x = 0.04.

2. Convert 0.04 to a fraction:

`0.04 = 4/100`

`0.04 = 1/25`

3. Write `1/25` as a power of 5:

`1/25 = 5^-2`

4. Therefore 5^x = 5^–2, so x = –2.

log₅ 0.04 = –2, i.e. in exponential form 5^–2 = 0.04.