What is the answer to log_{2x-5}(2x^2-2x-15)=2 ?

The answer to log_{2x-5}(2x^2-2x-15)=2 is x=4,x=5

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log_{2x-5}(2x^2-2x-15)=2

lo g_{2 x - 5} (2 x^{2} - 2 x - 15) = 2

x = 4, x = 5

Solution steps

lo g_{2 x - 5} (2 x^{2} - 2 x - 15) = 2

Apply log rules

\frac{ln ( 2 x ^{2} - 2 x - 15 )}{ln ( 2 x - 5 )} = 2

Multiply both sides by

ln (2 x - 5)

\frac{ln ( 2 x ^{2} - 2 x - 15 )}{ln ( 2 x - 5 )} ln (2 x - 5) = 2 ln (2 x - 5)

Simplify

ln (2 x^{2} - 2 x - 15) = 2 ln (2 x - 5)

Apply log rules

2 x^{2} - 2 x - 15 = (2 x - 5)^{2}

Solve

2 x^{2} - 2 x - 15 = (2 x - 5)^{2} : x = 4, x = 5

x = 4, x = 5

Verify Solutions:

x = 4

True

, x = 5

True

The solutions are

x = 4, x = 5

lo g_{12} (1 + \frac{r}{100}) = 3

lo g_{5} (x) - lo g_{5} (x - 1) = 1

lo g_{6} (x + 4) = 1 - lo g_{6} (x + 3)

lo g_{4} (x) = lo g_{x} (16)

3 ln (5 x + 1) - 8 = 44

What is the answer to log_{2x-5}(2x^2-2x-15)=2 ?
The answer to log_{2x-5}(2x^2-2x-15)=2 is x=4,x=5
Solve for x: log_{2x-5}(2x^2-2x-15)=2
The solution is x=4,x=5