What is the answer to log_{2x-3}(3x^2-18)=2 ?

The answer to log_{2x-3}(3x^2-18)=2 is x=9,x=3

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log_{2x-3}(3x^2-18)=2

lo g_{2 x - 3} (3 x^{2} - 18) = 2

x = 9, x = 3

Solution steps

lo g_{2 x - 3} (3 x^{2} - 18) = 2

Apply log rules

\frac{ln ( 3 x ^{2} - 18 )}{ln ( 2 x - 3 )} = 2

Multiply both sides by

ln (2 x - 3)

\frac{ln ( 3 x ^{2} - 18 )}{ln ( 2 x - 3 )} ln (2 x - 3) = 2 ln (2 x - 3)

Simplify

ln (3 x^{2} - 18) = 2 ln (2 x - 3)

Apply log rules

3 x^{2} - 18 = (2 x - 3)^{2}

Solve

3 x^{2} - 18 = (2 x - 3)^{2} : x = 9, x = 3

x = 9, x = 3

Verify Solutions:

x = 9

True

, x = 3

True

The solutions are

x = 9, x = 3

4 ln (5 x - 4) - 11 = 5

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

lo g_{3} ((x - 1)^{2}) = 2

lo g_{3} (x - 4) = 1 + lo g_{9} (x)

ln (1 + x) = 1

What is the answer to log_{2x-3}(3x^2-18)=2 ?
The answer to log_{2x-3}(3x^2-18)=2 is x=9,x=3
Solve for x: log_{2x-3}(3x^2-18)=2
The solution is x=9,x=3