Fill in the steps to solve the log log base x of (2x) ^3=6

x=2

Step-by-step explanation:

logx (2x) ^3 = 6

We can rewrite without the exponent

3 logx (2x) = 6

Divide by 3

3/3 logx (2x) = 6/3

logx (2x) = 2

Raise each side to the base x

x^ logx (2x) = x^ 2

2x = x^2

Subtract 2x from each side

2x-2x = x^2 - 2x

0 = x^2 - 2x

Factor an x

0 = x (x-2)

Using the zero product property

x = 0 x-2 = 0

x = 0 x=2

We cannot have a base of 0, so x cannot equal 0

x=2