Question

Steps to this log equation

Answer 1

I started out doing this the complicated way, but then I spotted the easy way,
and I realized how awkward and unhelpful my first method was.

log₃ ( 27/81 ) .

Before we even begin to worry about the log , let's reduce that ugly fraction
to lowest terms (simplest form).

Divide top and bottom by 27 :

log₃ (1/3) .  Now it's a lot less scary.

Definition of log₃ of (some number):
The power that 3 must be raised to in order to get the number.

What power do you have to raise 3 to in order to get 1/3 ?

Hint:  What does ' 3⁻¹ ' mean ?

' 3⁻¹ ' means 1/3 . 

So -1 is the power to which you have to raise 3 in order to get 1/3.

So the log₃ of (1/3) is -1 .

I suspect this is going in and out of focus as you read it.
Please go back and read it another 2 or 3 times, until it
snaps into focus.

Answer 2

$\log_3\frac{27}{81}=\\ \log_3\frac{1}{3}=\\ \log_33^{-1}=\\ -1$