What is the answer to log_{2x-6}(3x^2-10x-12)=2 ?

The answer to log_{2x-6}(3x^2-10x-12)=2 is x=6,x=8

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log_{2x-6}(3x^2-10x-12)=2

lo g_{2 x - 6} (3 x^{2} - 10 x - 12) = 2

x = 6, x = 8

Solution steps

lo g_{2 x - 6} (3 x^{2} - 10 x - 12) = 2

Apply log rules

\frac{ln ( 3 x ^{2} - 10 x - 12 )}{ln ( 2 x - 6 )} = 2

Multiply both sides by

ln (2 x - 6)

\frac{ln ( 3 x ^{2} - 10 x - 12 )}{ln ( 2 x - 6 )} ln (2 x - 6) = 2 ln (2 x - 6)

Simplify

ln (3 x^{2} - 10 x - 12) = 2 ln (2 x - 6)

Apply log rules

3 x^{2} - 10 x - 12 = (2 x - 6)^{2}

Solve

3 x^{2} - 10 x - 12 = (2 x - 6)^{2} : x = 6, x = 8

x = 6, x = 8

Verify Solutions:

x = 6

True

, x = 8

True

The solutions are

x = 6, x = 8

7 + lo g_{3} (5 x) = 8

3 = lo g_{x} (8)

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

lo g_{10} (x) (\frac{1}{8}) = 3

4.87 = - lo g_{10} (x)

What is the answer to log_{2x-6}(3x^2-10x-12)=2 ?
The answer to log_{2x-6}(3x^2-10x-12)=2 is x=6,x=8
Solve for x: log_{2x-6}(3x^2-10x-12)=2
The solution is x=6,x=8