Solve-for-x-3-x-2x-2-Mastermind-

Question Number 170946 by Mastermind last updated on 04/Jun/22

Solve for x :

3^{x} = 2 x + 2

Mastermind

Answered by mr W last updated on 04/Jun/22

3^{x} = 2 (x + 1)

3^{x + 1} = 6 (x + 1)

e^{(x + 1) \ln 3} = 6 (x + 1)

- (x + 1) \ln 3 e^{- (x + 1) \ln 3} = - \frac{\ln 3}{6}

- (x + 1) \ln 3 = W (- \frac{\ln 3}{6})

\Rightarrow x = - 1 - \frac{1}{\ln 3} W (- \frac{\ln 3}{6}) = {\begin{cases} 1.444561 \\ - 0.790109 \end{cases}

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