3-x-3x-x-

Question Number 66543 by hmamarques1994@gmail.com last updated on 17/Aug/19

3^{x} = 3 x

x = ?

Commented by gunawan last updated on 17/Aug/19

x = 1

Answered by mr W last updated on 17/Aug/19

3^{x} = 3 x

e^{x \ln 3} = 3 x

3 {x e}^{- x \ln 3} = 1

{x e}^{- x \ln 3} = \frac{1}{3}

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

\Rightarrow - x \ln 3 = W (- \frac{\ln 3}{3})

\Rightarrow x = - \frac{W (- \frac{\ln 3}{3})}{\ln 3} = {\begin{cases} - \frac{- 1.098612}{\ln 3} = 1 \\ - \frac{- 0.907473}{\ln 3} = 0.826017 \end{cases}

Commented by Cmr 237 last updated on 17/Aug/19

p l e a s e s i r i {d o n}^{.} t u n d e r s t a n d - y o u r 3^{r d} a n d 4^{t h} l i n e s d e m o n s t r a t i o n

Commented by mr W last updated on 17/Aug/19

t y p o i n t h i r d l i n e i s f i x e d n o w .

Answered by peter frank last updated on 17/Aug/19

u s e g r a p h

y = 3^{x} = 3 x

y = 3^{x}

y = 3 x