What is the answer to 3ln(x)=5x-6 ?

The answer to 3ln(x)=5x-6 is x=-(3\W_{-1}(-5/(3e^2)))/5 ,x=-(3\W_{0}(-5/(3e^2)))/5

Solve for x: 3ln(x)=5x-6

The solution is x=-(3\W_{-1}(-5/(3e^2)))/5 ,x=-(3\W_{0}(-5/(3e^2)))/5

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3 ln (x) = 5 x - 6

x = - \frac{3 W _{- 1} ( - \frac{5}{3 e ^{2}} )}{5}, x = - \frac{3 W _{0} ( - \frac{5}{3 e ^{2}} )}{5}

Decimal Notation

x = 1.40329 \dots, x = 0.18386 \dots

Solution steps

3 ln (x) = 5 x - 6

Divide both sides by

3

ln (x) = \frac{5 x - 6}{3}

f (x) = g (x),

then

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

e^{l n (x)} = e^{\frac{5 x - 6}{3}}

Simplify

e^{l n (x)} : x

x = e^{\frac{5 x - 6}{3}}

Solve

x = e^{\frac{5 x - 6}{3}} : x = - \frac{3 W _{- 1} ( - \frac{5}{3 e ^{2}} )}{5}, x = - \frac{3 W _{0} ( - \frac{5}{3 e ^{2}} )}{5}

x = - \frac{3 W _{- 1} ( - \frac{5}{3 e ^{2}} )}{5}, x = - \frac{3 W _{0} ( - \frac{5}{3 e ^{2}} )}{5}

Verify Solutions:

x = - \frac{3 W _{- 1} ( - \frac{5}{3 e ^{2}} )}{5}

True

, x = - \frac{3 W _{0} ( - \frac{5}{3 e ^{2}} )}{5}

True

The solutions are

x = - \frac{3 W _{- 1} ( - \frac{5}{3 e ^{2}} )}{5}, x = - \frac{3 W _{0} ( - \frac{5}{3 e ^{2}} )}{5}

lo g_{2} (x) - 16 lo g_{10} (x) = - 63

lo g_{b} (4) = 2

ln (x) = - 6

lo g_{10} (x) + lo g_{10} (x + 4) = 2

ln (x - 1) = 3

What is the answer to 3ln(x)=5x-6 ?
The answer to 3ln(x)=5x-6 is x=-(3\W_{-1}(-5/(3e^2)))/5 ,x=-(3\W_{0}(-5/(3e^2)))/5
Solve for x: 3ln(x)=5x-6
The solution is x=-(3\W_{-1}(-5/(3e^2)))/5 ,x=-(3\W_{0}(-5/(3e^2)))/5