What is the answer to log_{x+5}(2x^2+5x+1)=2 ?

The answer to log_{x+5}(2x^2+5x+1)=2 is x=8,x=-3

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log_{x+5}(2x^2+5x+1)=2

lo g_{x + 5} (2 x^{2} + 5 x + 1) = 2

x = 8, x = - 3

Solution steps

lo g_{x + 5} (2 x^{2} + 5 x + 1) = 2

Apply log rules

\frac{ln ( 2 x ^{2} + 5 x + 1 )}{ln ( x + 5 )} = 2

Multiply both sides by

ln (x + 5)

\frac{ln ( 2 x ^{2} + 5 x + 1 )}{ln ( x + 5 )} ln (x + 5) = 2 ln (x + 5)

Simplify

ln (2 x^{2} + 5 x + 1) = 2 ln (x + 5)

Apply log rules

2 x^{2} + 5 x + 1 = (x + 5)^{2}

Solve

2 x^{2} + 5 x + 1 = (x + 5)^{2} : x = 8, x = - 3

x = 8, x = - 3

Verify Solutions:

x = 8

True

, x = - 3

True

The solutions are

x = 8, x = - 3

lo g_{9} (x) + lo g_{9} (12) = \frac{1}{2} lo g_{9} (100)

5 lo g_{3} (x + 1) + 6 = 7

lo g_{x} (4) = \frac{- 2}{5}

2 lo g_{10} (7 x) + 1 = 4

20 lo g_{10} (x) = - 6.628

What is the answer to log_{x+5}(2x^2+5x+1)=2 ?
The answer to log_{x+5}(2x^2+5x+1)=2 is x=8,x=-3
Solve for x: log_{x+5}(2x^2+5x+1)=2
The solution is x=8,x=-3