What is the answer to log_{x}(12-x)=2 ?

The answer to log_{x}(12-x)=2 is x=3

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log_{x}(12-x)=2

lo g_{x} (12 - x) = 2

x = 3

Solution steps

lo g_{x} (12 - x) = 2

Apply log rules

\frac{ln ( 12 - x )}{ln ( x )} = 2

Multiply both sides by

ln (x)

\frac{ln ( 12 - x )}{ln ( x )} ln (x) = 2 ln (x)

Simplify

ln (12 - x) = 2 ln (x)

Apply log rules

12 - x = x^{2}

Solve

12 - x = x^{2} : x = 3, x = - 4

x = 3, x = - 4

Verify Solutions:

x = 3

True

, x = - 4

False

The solution is

x = 3

4 ln (3 x) = 15

lo g_{y} (y - 2) + lo g_{y} (y + 5) = 2

lo g_{x} (\frac{1}{16}) = - 4

30 = 10 lo g_{10} (x)

2 lo g_{3} (n) + 3 lo g_{27} (n) = 15