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

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

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

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

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ln (3 x + 2) = 3 x

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

Solution steps

ln (3 x + 2) = 3 x

f (x) = g (x),

then

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

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

Simplify

e^{l n (3 x + 2)} : 3 x + 2

3 x + 2 = e^{3 x}

Solve

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

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

Verify Solutions:

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

True

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

True

The solutions are

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

lo g_{10} (3 x) = - lo g_{10} (9)

2 lo g_{10} (x) - 2 lo g_{10} (2) = 1

lo g_{2} (n) = 2147483648

2 ln (x - 4) + ln (x + 9) = 3 ln (x)

\frac{x + n}{2 ln ( x ) - n} = 0

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