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

The answer to log_{2x}(3x^2+3x-2)=2 is x=1,x=2

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

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

x = 1, x = 2

Solution steps

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

Apply log rules

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

Multiply both sides by

ln (2 x)

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

Simplify

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

Apply log rules

3 x^{2} + 3 x - 2 = 4 x^{2}

Solve

3 x^{2} + 3 x - 2 = 4 x^{2} : x = 1, x = 2

x = 1, x = 2

Verify Solutions:

x = 1

True

, x = 2

True

The solutions are

x = 1, x = 2

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

lo g_{x} (3) = 2.23

lo g_{4} (2 x - 3) + lo g_{4} (5 - x) = 2

x, ln (x + 4) = 4

lo g_{10} (\frac{1}{x}) = 8.78

What is the answer to log_{2x}(3x^2+3x-2)=2 ?
The answer to log_{2x}(3x^2+3x-2)=2 is x=1,x=2
Solve for x: log_{2x}(3x^2+3x-2)=2
The solution is x=1,x=2