What is the answer to log_{x+8}(2x^2-5x-8)=2 ?

The answer to log_{x+8}(2x^2-5x-8)=2 is x=24,x=-3

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log_{x+8}(2x^2-5x-8)=2

lo g_{x + 8} (2 x^{2} - 5 x - 8) = 2

x = 24, x = - 3

Solution steps

lo g_{x + 8} (2 x^{2} - 5 x - 8) = 2

Apply log rules

\frac{ln ( 2 x ^{2} - 5 x - 8 )}{ln ( x + 8 )} = 2

Multiply both sides by

ln (x + 8)

\frac{ln ( 2 x ^{2} - 5 x - 8 )}{ln ( x + 8 )} ln (x + 8) = 2 ln (x + 8)

Simplify

ln (2 x^{2} - 5 x - 8) = 2 ln (x + 8)

Apply log rules

2 x^{2} - 5 x - 8 = (x + 8)^{2}

Solve

2 x^{2} - 5 x - 8 = (x + 8)^{2} : x = 24, x = - 3

x = 24, x = - 3

Verify Solutions:

x = 24

True

, x = - 3

True

The solutions are

x = 24, x = - 3

lo g_{x} (x) = 1

lo g_{x} (32) = 4

lo g_{5} (2 x + 7) = 2

ln (8 x) + 3 = ln (2 x + 6)

lo g_{7} (\frac{3 x}{4} - 2) = 0

What is the answer to log_{x+8}(2x^2-5x-8)=2 ?
The answer to log_{x+8}(2x^2-5x-8)=2 is x=24,x=-3
Solve for x: log_{x+8}(2x^2-5x-8)=2
The solution is x=24,x=-3