What is the answer to log_{x-2}(3x-2)=2 ?

The answer to log_{x-2}(3x-2)=2 is x=6

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log_{x-2}(3x-2)=2

lo g_{x - 2} (3 x - 2) = 2

x = 6

Solution steps

lo g_{x - 2} (3 x - 2) = 2

Apply log rules

\frac{ln ( 3 x - 2 )}{ln ( x - 2 )} = 2

Multiply both sides by

ln (x - 2)

\frac{ln ( 3 x - 2 )}{ln ( x - 2 )} ln (x - 2) = 2 ln (x - 2)

Simplify

ln (3 x - 2) = 2 ln (x - 2)

Apply log rules

3 x - 2 = (x - 2)^{2}

Solve

3 x - 2 = (x - 2)^{2} : x = 6, x = 1

x = 6, x = 1

Verify Solutions:

x = 6

True

, x = 1

False

The solution is

x = 6

ln (x + 1) = 8

ln (x + 1) = 7

x = ln (1 + x)

x, ln (y) = ln (x) + C

ln (x + 8) + ln (x - 2) = 2 ln (x)

What is the answer to log_{x-2}(3x-2)=2 ?
The answer to log_{x-2}(3x-2)=2 is x=6
Solve for x: log_{x-2}(3x-2)=2
The solution is x=6