What is the answer to log_{x+6}(2x^2+3x)=2 ?

The answer to log_{x+6}(2x^2+3x)=2 is x=-3,x=12

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log_{x+6}(2x^2+3x)=2

lo g_{x + 6} (2 x^{2} + 3 x) = 2

x = - 3, x = 12

Solution steps

lo g_{x + 6} (2 x^{2} + 3 x) = 2

Apply log rules

\frac{ln ( 2 x ^{2} + 3 x )}{ln ( x + 6 )} = 2

Multiply both sides by

ln (x + 6)

\frac{ln ( 2 x ^{2} + 3 x )}{ln ( x + 6 )} ln (x + 6) = 2 ln (x + 6)

Simplify

ln (2 x^{2} + 3 x) = 2 ln (x + 6)

Apply log rules

2 x^{2} + 3 x = (x + 6)^{2}

Solve

2 x^{2} + 3 x = (x + 6)^{2} : x = - 3, x = 12

x = - 3, x = 12

Verify Solutions:

x = - 3

True

, x = 12

True

The solutions are

x = - 3, x = 12

lo g_{3} (x) + 2 lo g_{9} (x) = 4

0.53 = ln (y)

\frac{1}{2} = lo g_{x} (10)

x, ln (x) + ln (x + 1) = 0

lo g_{2} (2 x) = lo g_{4} (x)

What is the answer to log_{x+6}(2x^2+3x)=2 ?
The answer to log_{x+6}(2x^2+3x)=2 is x=-3,x=12
Solve for x: log_{x+6}(2x^2+3x)=2
The solution is x=-3,x=12