What is the answer to log_{3-2x}(6x^2-11x+6)=2 ?

The answer to log_{3-2x}(6x^2-11x+6)=2 is x=-3/2

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log_{3-2x}(6x^2-11x+6)=2

lo g_{3 - 2 x} (6 x^{2} - 11 x + 6) = 2

x = - \frac{3}{2}

Decimal Notation

x = - 1.5

Solution steps

lo g_{3 - 2 x} (6 x^{2} - 11 x + 6) = 2

Apply log rules

\frac{ln ( 6 x ^{2} - 11 x + 6 )}{ln ( 3 - 2 x )} = 2

Multiply both sides by

ln (3 - 2 x)

\frac{ln ( 6 x ^{2} - 11 x + 6 )}{ln ( 3 - 2 x )} ln (3 - 2 x) = 2 ln (3 - 2 x)

Simplify

ln (6 x^{2} - 11 x + 6) = 2 ln (3 - 2 x)

Apply log rules

6 x^{2} - 11 x + 6 = (3 - 2 x)^{2}

Solve

6 x^{2} - 11 x + 6 = (3 - 2 x)^{2} : x = 1, x = - \frac{3}{2}

x = 1, x = - \frac{3}{2}

Verify Solutions:

x = 1

False

, x = - \frac{3}{2}

True

The solution is

x = - \frac{3}{2}

- 1 = lo g_{10} (x)

ln (x) = - x

ln (x) = - 4

ln (x) = - 5

lo g_{x} (0.004) = 2

What is the answer to log_{3-2x}(6x^2-11x+6)=2 ?
The answer to log_{3-2x}(6x^2-11x+6)=2 is x=-3/2
Solve for x: log_{3-2x}(6x^2-11x+6)=2
The solution is x=-3/2