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

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