What is the answer to log_{x}(8-2x)=2 ?

The answer to log_{x}(8-2x)=2 is x=2

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log_{x}(8-2x)=2

lo g_{x} (8 - 2 x) = 2

x = 2

Solution steps

lo g_{x} (8 - 2 x) = 2

Apply log rules

\frac{ln ( 8 - 2 x )}{ln ( x )} = 2

Multiply both sides by

ln (x)

\frac{ln ( 8 - 2 x )}{ln ( x )} ln (x) = 2 ln (x)

Simplify

ln (8 - 2 x) = 2 ln (x)

Apply log rules

8 - 2 x = x^{2}

Solve

8 - 2 x = x^{2} : x = 2, x = - 4

x = 2, x = - 4

Verify Solutions:

x = 2

True

, x = - 4

False

The solution is

x = 2

ln (2 x + 1) - ln (x - 1) = 4

lo g_{2} (\frac{x}{2}) = 5

x, ln (y) = lo g_{10} (x)

y, z - ln (y) = 0

x, ln (y) = 3 ln (x) + c