What is the answer to log_{x+5}(2x^2-7x+7)=2 ?

The answer to log_{x+5}(2x^2-7x+7)=2 is x=18,x=-1

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log_{x+5}(2x^2-7x+7)=2

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

x = 18, x = - 1

Solution steps

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

Apply log rules

\frac{ln ( 2 x ^{2} - 7 x + 7 )}{ln ( x + 5 )} = 2

Multiply both sides by

ln (x + 5)

\frac{ln ( 2 x ^{2} - 7 x + 7 )}{ln ( x + 5 )} ln (x + 5) = 2 ln (x + 5)

Simplify

ln (2 x^{2} - 7 x + 7) = 2 ln (x + 5)

Apply log rules

2 x^{2} - 7 x + 7 = (x + 5)^{2}

Solve

2 x^{2} - 7 x + 7 = (x + 5)^{2} : x = 18, x = - 1

x = 18, x = - 1

Verify Solutions:

x = 18

True

, x = - 1

True

The solutions are

x = 18, x = - 1

lo g_{x} (\frac{4}{9}) = - 2

lo g_{10} (x) - lo g_{10} (x + 2) = 1

lo g_{10} (x + 6) = lo g_{10} (x) + lo g_{10} (6)

5 x + 3 ln (x - 4) = 25

lo g_{2} (\frac{x}{4}) = 1

What is the answer to log_{x+5}(2x^2-7x+7)=2 ?
The answer to log_{x+5}(2x^2-7x+7)=2 is x=18,x=-1
Solve for x: log_{x+5}(2x^2-7x+7)=2
The solution is x=18,x=-1