What is the answer to log_{x-2}(2x^2-11x+16)=2 ?

The answer to log_{x-2}(2x^2-11x+16)=2 is x=4

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log_{x-2}(2x^2-11x+16)=2

lo g_{x - 2} (2 x^{2} - 11 x + 16) = 2

x = 4

Solution steps

lo g_{x - 2} (2 x^{2} - 11 x + 16) = 2

Apply log rules

\frac{ln ( 2 x ^{2} - 11 x + 16 )}{ln ( x - 2 )} = 2

Multiply both sides by

ln (x - 2)

\frac{ln ( 2 x ^{2} - 11 x + 16 )}{ln ( x - 2 )} ln (x - 2) = 2 ln (x - 2)

Simplify

ln (2 x^{2} - 11 x + 16) = 2 ln (x - 2)

Apply log rules

2 x^{2} - 11 x + 16 = (x - 2)^{2}

Solve

2 x^{2} - 11 x + 16 = (x - 2)^{2} : x = 4, x = 3

x = 4, x = 3

Verify Solutions:

x = 4

True

, x = 3

False

The solution is

x = 4

lo g_{10} (0.5 x) = - 6

lo g_{6} (\frac{x + 4}{x - 1}) = 1

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

lo g_{5} (x - 1) = 2

ln (x + 3) - ln (x - 1) = ln (3)

What is the answer to log_{x-2}(2x^2-11x+16)=2 ?
The answer to log_{x-2}(2x^2-11x+16)=2 is x=4
Solve for x: log_{x-2}(2x^2-11x+16)=2
The solution is x=4