What is the answer to log_{x+6}(2x^2-4x)=2 ?

The answer to log_{x+6}(2x^2-4x)=2 is x=-2,x=18

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log_{x+6}(2x^2-4x)=2

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

x = - 2, x = 18

Solution steps

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

Apply log rules

\frac{ln ( 2 x ^{2} - 4 x )}{ln ( x + 6 )} = 2

Multiply both sides by

ln (x + 6)

\frac{ln ( 2 x ^{2} - 4 x )}{ln ( x + 6 )} ln (x + 6) = 2 ln (x + 6)

Simplify

ln (2 x^{2} - 4 x) = 2 ln (x + 6)

Apply log rules

2 x^{2} - 4 x = (x + 6)^{2}

Solve

2 x^{2} - 4 x = (x + 6)^{2} : x = - 2, x = 18

x = - 2, x = 18

Verify Solutions:

x = - 2

True

, x = 18

True

The solutions are

x = - 2, x = 18

lo g_{2} (x + 1) + lo g_{2} (x - 2) = 3

ln (x) = 900

lo g_{10} (x^{2} + 36) = 2

ln (x) = 5.014055365

0.8 = ln (x)

What is the answer to log_{x+6}(2x^2-4x)=2 ?
The answer to log_{x+6}(2x^2-4x)=2 is x=-2,x=18
Solve for x: log_{x+6}(2x^2-4x)=2
The solution is x=-2,x=18