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

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

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log_{x}(6-x)=2

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

x = 2

Solution steps

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

Apply log rules

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

Multiply both sides by

ln (x)

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

Simplify

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

Apply log rules

6 - x = x^{2}

Solve

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

x = 2, x = - 3

Verify Solutions:

x = 2

True

, x = - 3

False

The solution is

x = 2

lo g_{10} (2 x - 1) = \frac{1}{2}

lo g_{10} (x) = - 6

lo g_{10} (x) = 11

lo g_{10} (4 x) = 3

x = lo g_{2} (x)