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

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

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

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

x = 2

Solution steps

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

Apply log rules

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

Multiply both sides by

ln (x)

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

Simplify

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

Apply log rules

- x + 6 = x^{2}

Solve

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

x = 2, x = - 3

Verify Solutions:

x = 2

True

, x = - 3

False

The solution is

x = 2

- 2 = lo g_{10} (x)

lo g_{4} (y) = 2

lo g_{27} (x) = \frac{2}{3}

2.4 = lo g_{10} (x)

ln (x - 2) - ln (2 x^{1}) - 3 = 0