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

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

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

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

x = - 4, x = - 3

Solution steps

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

Apply log rules

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

Multiply both sides by

ln (- 2 x - 3)

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

Simplify

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

Apply log rules

2 x^{2} - 2 x - 15 = (- 2 x - 3)^{2}

Solve

2 x^{2} - 2 x - 15 = (- 2 x - 3)^{2} : x = - 4, x = - 3

x = - 4, x = - 3

Verify Solutions:

x = - 4

True

, x = - 3

True

The solutions are

x = - 4, x = - 3

x, lo g_{3} (x) = 3

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

u, lo g_{u} (\frac{15}{16}) = v

lo g_{2} (6 \cdot 2^{2 n + 1} - 6) = n

lo g_{10} (x) - lo g_{10} (9) = 1

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