Question

Express the following in exponential form:

`log_4  1/32 = - 5/2`

Answer 1

Given: `log_4  1/32 = - 5/2`

Step-wise calculation: 

By definition of logarithm (log_ab = c ⇔ a^c = b), 

We rewrite: `4^(-5/2) = 1/32`

Then `4^(-5/2) = (4^(1/2))^(-5)`

`4^(-5/2) =  (sqrt4)^(-5)`

`4^(-5/2) = 2^(-5)`

`4^(-5/2) = 1/32`