What is the answer to log_{x}(-x+90)=2 ?

The answer to log_{x}(-x+90)=2 is x=9

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log_{x}(-x+90)=2

lo g_{x} (- x + 90) = 2

x = 9

Solution steps

lo g_{x} (- x + 90) = 2

Apply log rules

\frac{ln ( - x + 90 )}{ln ( x )} = 2

Multiply both sides by

ln (x)

\frac{ln ( - x + 90 )}{ln ( x )} ln (x) = 2 ln (x)

Simplify

ln (- x + 90) = 2 ln (x)

Apply log rules

- x + 90 = x^{2}

Solve

- x + 90 = x^{2} : x = 9, x = - 10

x = 9, x = - 10

Verify Solutions:

x = 9

True

, x = - 10

False

The solution is

x = 9

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lo g_{2} (x) + lo g_{2} (4 x) - 6 = 0

lo g_{x + 3} (3 x^{2} - 2 x + 9) = 2

x, y^{6} = ln (x y)

3 ln (16 x^{2} - 8 y) = 0