What is the answer to log_{-2x-4}(2x^2-14)=2 ?

The answer to log_{-2x-4}(2x^2-14)=2 is x=-3,x=-5

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log_{-2x-4}(2x^2-14)=2

lo g_{- 2 x - 4} (2 x^{2} - 14) = 2

x = - 3, x = - 5

Solution steps

lo g_{- 2 x - 4} (2 x^{2} - 14) = 2

Apply log rules

\frac{ln ( 2 x ^{2} - 14 )}{ln ( - 2 x - 4 )} = 2

Multiply both sides by

ln (- 2 x - 4)

\frac{ln ( 2 x ^{2} - 14 )}{ln ( - 2 x - 4 )} ln (- 2 x - 4) = 2 ln (- 2 x - 4)

Simplify

ln (2 x^{2} - 14) = 2 ln (- 2 x - 4)

Apply log rules

2 x^{2} - 14 = (- 2 x - 4)^{2}

Solve

2 x^{2} - 14 = (- 2 x - 4)^{2} : x = - 3, x = - 5

x = - 3, x = - 5

Verify Solutions:

x = - 3

True

, x = - 5

True

The solutions are

x = - 3, x = - 5

x, 3.5 = 3.75 + lo g_{10} (x)

lo g_{\frac{1}{3}} (x) = \frac{1}{27}

(lo g_{10} (x))^{2} + 2 lo g_{10} (x) = 3

lo g_{10} (x) + lo g_{10} (x + 5) = 1

lo g_{10} (x) + lo g_{10} (x + 5) = 6

What is the answer to log_{-2x-4}(2x^2-14)=2 ?
The answer to log_{-2x-4}(2x^2-14)=2 is x=-3,x=-5
Solve for x: log_{-2x-4}(2x^2-14)=2
The solution is x=-3,x=-5