Question

Evaluate the following by converting into exponential form:

log_0.5 64

Answer 1

Given: log_0.5 64

Step-wise calculation:

1. Let x = log_0.5 64,

So (0.5)^x = 64.

2. Write 0.5 as `1/2`: 

`(1/2)^x = 64`

3. Express both sides with base 2:

`(1/2)^x = 2^(-x)` and 64 = 2⁶

4. So 2^–x = 2⁶

⇒ –x = 6

⇒ x = –6