Question

Evaluate the following:

log₁₆ 32 – log₉ 27

Answer 1

Given: log₁₆ 32 – log₉ 27

Step-wise calculation:

1. log₁₆ 32

= `(log_2 32)/(log_2 16)`

= `5/4`

Because 32 = 2⁵ and 16 = 2⁴.

2. log₉ 27 

= `(log_3 27)/(log_3 9)`

= `3/2`

Because 27 = 3³ and 9 = 3².

3. Subtract:

`5/4 - 3/2`

= `5/4 - 6/4`

= `-1/4`

`log_16 32 - log_9 27 = -1/4 (-0.25)`.