Question

log₄ 32 – log₈ 32 is equal to ______.

Options

• `1/3`

• `1/2`

• `7/6`

• `5/6`

Answer 1

log₄ 32 – log₈ 32 is equal to `underlinebb(5/6)`.

Explanation:

Write 32 = 2⁵.

Then log₄ 32

= log₄ (2⁵) 

= 5 × log₄ 2 

= `5 xx (1/2)` 

= `5/2`

log₈ 32 

= log₈ (2⁵) 

= 5 × log₈ 2 

= `5 xx (1/3)` 

= `5/3`

So log₄ 32 − log₈ 32 

= `5/2 - 5/3` 

= `(15 - 10)/6` 

= `5/6`