What is the answer to 5ln(3x-2)=15 ?

The answer to 5ln(3x-2)=15 is x=(e^3+2)/3

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5ln(3x-2)=15

5 ln (3 x - 2) = 15

x = \frac{e ^{3} + 2}{3}

Decimal Notation

x = 7.36184 \dots

Solution steps

5 ln (3 x - 2) = 15

Divide both sides by

5

ln (3 x - 2) = 3

Apply log rules

3 x - 2 = e^{3}

Solve

3 x - 2 = e^{3} : x = \frac{e ^{3} + 2}{3}

x = \frac{e ^{3} + 2}{3}

Verify Solutions:

x = \frac{e ^{3} + 2}{3}

True

The solution is

x = \frac{e ^{3} + 2}{3}

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

- 2 \cdot lo g_{3} (3 - x) + 1 = 0

\frac{ln ( x )}{e} = 0

x, ln (x) = 7

x, ln (x) = 6