What is the solution to the equation below? log64x^2-log6x=2

x=1/2

x=3/2

x=3

x=9

First, we need to put the conditions: 4x^2 >0 which is obviously true

x>0

We will apply the formulas:

loga (x) - loga (y) = loga (x/y)

and

if loga (x) = b then x = a^b

log6 (4x^2) - log6 (x) = 2

Applying first formula

log6 (4x^2/x) = 2

log6 (4x) = 2

Applying the second formula:

4x = 36

x=9