What is the answer to log_{x+7}(3x^2+6x-15)=2 ?

The answer to log_{x+7}(3x^2+6x-15)=2 is x=8,x=-4

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log_{x+7}(3x^2+6x-15)=2

lo g_{x + 7} (3 x^{2} + 6 x - 15) = 2

x = 8, x = - 4

Solution steps

lo g_{x + 7} (3 x^{2} + 6 x - 15) = 2

Apply log rules

\frac{ln ( 3 x ^{2} + 6 x - 15 )}{ln ( x + 7 )} = 2

Multiply both sides by

ln (x + 7)

\frac{ln ( 3 x ^{2} + 6 x - 15 )}{ln ( x + 7 )} ln (x + 7) = 2 ln (x + 7)

Simplify

ln (3 x^{2} + 6 x - 15) = 2 ln (x + 7)

Apply log rules

3 x^{2} + 6 x - 15 = (x + 7)^{2}

Solve

3 x^{2} + 6 x - 15 = (x + 7)^{2} : x = 8, x = - 4

x = 8, x = - 4

Verify Solutions:

x = 8

True

, x = - 4

True

The solutions are

x = 8, x = - 4

y, y = ln (x y)

lo g_{2 x} (x^{2} + 9 x - 6) = 2

lo g_{0.2} (2 x - 3) = - 1

ln (x) = \frac{x}{2}

0.1 x = ln (1 + 0.15 x)

What is the answer to log_{x+7}(3x^2+6x-15)=2 ?
The answer to log_{x+7}(3x^2+6x-15)=2 is x=8,x=-4
Solve for x: log_{x+7}(3x^2+6x-15)=2
The solution is x=8,x=-4