What is the answer to ln(3x^2+x-2)=3ln(3x-2) ?

The answer to ln(3x^2+x-2)=3ln(3x-2) is x=(13+sqrt(61))/(18)

Solve for x: ln(3x^2+x-2)=3ln(3x-2)

The solution is x=(13+sqrt(61))/(18)

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

x = \frac{13 + 61}{18}

Decimal Notation

x = 1.15612 \dots

Solution steps

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

Apply log rules

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

Solve

3 x^{2} + x - 2 = (3 x - 2)^{3} : x = \frac{2}{3}, x = \frac{13 + 61}{18}, x = \frac{13 - 61}{18}

x = \frac{2}{3}, x = \frac{13 + 61}{18}, x = \frac{13 - 61}{18}

Verify Solutions:

x = \frac{2}{3}

False

, x = \frac{13 + 61}{18}

True

, x = \frac{13 - 61}{18}

False

The solution is

x = \frac{13 + 61}{18}

lo g_{10} (10 c) = 1

\frac{1}{3} ln (x) = ln (8)

x, c = ln (x + c t)

ln (x + 1) + ln (x + 3) = ln (x + 7)

lo g_{10} (x - 10) = 1

What is the answer to ln(3x^2+x-2)=3ln(3x-2) ?
The answer to ln(3x^2+x-2)=3ln(3x-2) is x=(13+sqrt(61))/(18)
Solve for x: ln(3x^2+x-2)=3ln(3x-2)
The solution is x=(13+sqrt(61))/(18)