Solve the equation:

2logx-log (x-2) = 2log3

x=6 x=3

Step-by-step explanation:

2logx-log (x-2) = 2log3

We know that a log b = log b^a

logx^2-log (x-2) = log3^2

logx^2-log (x-2) = log9

subtract log 9 from each side

logx^2-log (x-2) - log9=0

We know that log a - log b = log (a/b)

log (x^2/9 (x-2)) = 0

Raise each side to the power of 10 to get rid of the log

10 ^log (x^2/9 (x-2)) = 10 ^0

10^ log cancels and 10^0 = 1

(x^2/9 (x-2)) = 1

Multiply each side by 9 (x-2)

x^2 = 9 (x-2)

Subtract 9 (x-2) from each side

x^2 - 9 (x-2) = 9 (x-2) - 9 (x-2)

x^2 - 9 (x-2) = 0

Distribute

x^2 - 9x + 18 = 0

Factor

(x-6) (x-3) = 0

Using the zero product property

x-6 = 0 x-3 = 0

x=6 x=3