Logarithm of a Quotient

log₂ 32/√8 = log₂ 32 - log₂ √8

32 = 2⁵

√8 = √2³

Power

√2³ = 2^3/2

Rational Exponent

log₂ 2⁵ = 5 log₂ 2

-log₂ 2^3/2 = -[3/2] log₂ 2

Logarithm of a Power

log₂ 2 = 1

Logarithm of Itself

5⋅1 = 5
-[3/2]⋅1 = -3/2

5 = 10/2

10/2 - 3/2 = 7/2

So 7/2 is the answer.

Every term has log₆.
So combine these logs into log₆.

First write log₆ (.

log₆ 9

The sign is plus.

So write 9.

-log₆ 15

The sign is minus.

So divide 15.

+log₆ 10

The sign is plus.

So multiply 10.

Logarithm of a Product

So
log₆ 9 - log₆ 15 + log₆ 10
= log₆ ([9/15]⋅10).

Reduce 10 to, 10/5, 2
and reduce 15 to, 15/5, 3.

9/3 = 3

3⋅2 = 6

log₆ 6 = 1

So 1 is the answer.