What is the answer to log_{2x-5}(3x^2-7x-11)=2 ?

The answer to log_{2x-5}(3x^2-7x-11)=2 is x=4,x=9

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log_{2x-5}(3x^2-7x-11)=2

lo g_{2 x - 5} (3 x^{2} - 7 x - 11) = 2

x = 4, x = 9

Solution steps

lo g_{2 x - 5} (3 x^{2} - 7 x - 11) = 2

Apply log rules

\frac{ln ( 3 x ^{2} - 7 x - 11 )}{ln ( 2 x - 5 )} = 2

Multiply both sides by

ln (2 x - 5)

\frac{ln ( 3 x ^{2} - 7 x - 11 )}{ln ( 2 x - 5 )} ln (2 x - 5) = 2 ln (2 x - 5)

Simplify

ln (3 x^{2} - 7 x - 11) = 2 ln (2 x - 5)

Apply log rules

3 x^{2} - 7 x - 11 = (2 x - 5)^{2}

Solve

3 x^{2} - 7 x - 11 = (2 x - 5)^{2} : x = 4, x = 9

x = 4, x = 9

Verify Solutions:

x = 4

True

, x = 9

True

The solutions are

x = 4, x = 9

ln (x^{0.5}) = (ln (x))^{0.5}

ln (7 x + e) = 9

2.85 = - lo g_{10} (x)

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

4 lo g_{x} (2) - lo g_{2} (x) = 3

What is the answer to log_{2x-5}(3x^2-7x-11)=2 ?
The answer to log_{2x-5}(3x^2-7x-11)=2 is x=4,x=9
Solve for x: log_{2x-5}(3x^2-7x-11)=2
The solution is x=4,x=9