What is the answer to ln(3x+9)=2x-3 ?

The answer to ln(3x+9)=2x-3 is x=-(\W_{-1}(-2/(3e^9))+6)/2 ,x=-(\W_{0}(-2/(3e^9))+6)/2

Solve for x: ln(3x+9)=2x-3

The solution is x=-(\W_{-1}(-2/(3e^9))+6)/2 ,x=-(\W_{0}(-2/(3e^9))+6)/2

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ln (3 x + 9) = 2 x - 3

x = - \frac{W _{- 1} ( - \frac{2}{3 e ^{9}} ) + 6}{2}, x = - \frac{W _{0} ( - \frac{2}{3 e ^{9}} ) + 6}{2}

Decimal

x = 2.94017 \dots, x = - 2.99995 \dots

Solution steps

ln (3 x + 9) = 2 x - 3

f (x) = g (x),

then

a^{f (x)} = a^{g (x)}

e^{l n (3 x + 9)} = e^{2 x - 3}

Simplify

e^{l n (3 x + 9)} : 3 x + 9

3 x + 9 = e^{2 x - 3}

Solve

3 x + 9 = e^{2 x - 3} : x = - \frac{W _{- 1} ( - \frac{2}{3 e ^{9}} ) + 6}{2}, x = - \frac{W _{0} ( - \frac{2}{3 e ^{9}} ) + 6}{2}

x = - \frac{W _{- 1} ( - \frac{2}{3 e ^{9}} ) + 6}{2}, x = - \frac{W _{0} ( - \frac{2}{3 e ^{9}} ) + 6}{2}

Verify Solutions:

x = - \frac{W _{- 1} ( - \frac{2}{3 e ^{9}} ) + 6}{2}

True

, x = - \frac{W _{0} ( - \frac{2}{3 e ^{9}} ) + 6}{2}

True

The solutions are

x = - \frac{W _{- 1} ( - \frac{2}{3 e ^{9}} ) + 6}{2}, x = - \frac{W _{0} ( - \frac{2}{3 e ^{9}} ) + 6}{2}

lo g_{2} ((2 x^{2} + 7 x) + 9) = 3

lo g_{5} (5 x) + lo g_{5} (x) = 0

lo g_{2} (x) = 12

lo g_{4} (x^{2} + 15) = 3

\frac{- 3 ln ( x ) + 1}{x ^{4}} = 0

What is the answer to ln(3x+9)=2x-3 ?
The answer to ln(3x+9)=2x-3 is x=-(\W_{-1}(-2/(3e^9))+6)/2 ,x=-(\W_{0}(-2/(3e^9))+6)/2
Solve for x: ln(3x+9)=2x-3
The solution is x=-(\W_{-1}(-2/(3e^9))+6)/2 ,x=-(\W_{0}(-2/(3e^9))+6)/2