What is the answer to log_{x+6}(2x^2+8)=2 ?

The answer to log_{x+6}(2x^2+8)=2 is x=-2,x=14

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log_{x+6}(2x^2+8)=2

lo g_{x + 6} (2 x^{2} + 8) = 2

x = - 2, x = 14

Solution steps

lo g_{x + 6} (2 x^{2} + 8) = 2

Apply log rules

\frac{ln ( 2 x ^{2} + 8 )}{ln ( x + 6 )} = 2

Multiply both sides by

ln (x + 6)

\frac{ln ( 2 x ^{2} + 8 )}{ln ( x + 6 )} ln (x + 6) = 2 ln (x + 6)

Simplify

ln (2 x^{2} + 8) = 2 ln (x + 6)

Apply log rules

2 x^{2} + 8 = (x + 6)^{2}

Solve

2 x^{2} + 8 = (x + 6)^{2} : x = - 2, x = 14

x = - 2, x = 14

Verify Solutions:

x = - 2

True

, x = 14

True

The solutions are

x = - 2, x = 14

w, q = 2 ln (\frac{w}{2 p})

lo g_{2} (x - 1) = 4

lo g_{10} (5 x) = lo g_{10} (2 x + 9)

lo g_{5} (x + 10) + 7 = 9

lo g_{b} (100) = 3

What is the answer to log_{x+6}(2x^2+8)=2 ?
The answer to log_{x+6}(2x^2+8)=2 is x=-2,x=14
Solve for x: log_{x+6}(2x^2+8)=2
The solution is x=-2,x=14