What is the answer to log_{x}(6x-9)=2 ?

The answer to log_{x}(6x-9)=2 is x=3

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log_{x}(6x-9)=2

lo g_{x} (6 x - 9) = 2

x = 3

Solution steps

lo g_{x} (6 x - 9) = 2

Apply log rules

\frac{ln ( 6 x - 9 )}{ln ( x )} = 2

Multiply both sides by

ln (x)

\frac{ln ( 6 x - 9 )}{ln ( x )} ln (x) = 2 ln (x)

Simplify

ln (6 x - 9) = 2 ln (x)

Apply log rules

6 x - 9 = x^{2}

Solve

6 x - 9 = x^{2} : x = 3

x = 3

Verify Solutions:

x = 3

True

The solution is

x = 3

lo g_{6} (x) + lo g_{6} (x - 5) = 2

lo g_{x} (8) = \frac{3}{4}

lo g_{7} (x) = 3

ln (x) + ln (x - 2) = ln (4)

ln (x - 1) + ln (x + 2) = 1