Solve-for-x-3-2x-18x-please-i-need-workings-

Question Number 10317 by Tawakalitu ayo mi last updated on 03/Feb/17

Solve for x .

3^{2 x} = 18 x

please i need workings .

Answered by mrW1 last updated on 03/Feb/17

{(3^{2})}^{x} = 18 x

9^{x} = 18 x

e^{x \ln 9} = 18 x

1 = \frac{18}{- \ln 9} (- x \ln 9) e^{- x \ln 9}

(- x \ln 9) e^{- x \ln 9} = - \frac{\ln 9}{18}

- x \ln 9 = W (- \frac{\ln 9}{18}) w i t h W = L a m b e r t W f u n c t i o n

x = - \frac{W (- \frac{\ln 9}{18})}{\ln 9} = - \frac{W (- 0.122068)}{2.197225}

= {\begin{cases} - \frac{- 0.140479}{2.197225} = 0.063935 \\ - \frac{- 3.295837}{2.197225} = 1.5 \end{cases}

Commented by Tawakalitu ayo mi last updated on 04/Feb/17

God bless you sir .

Answered by arge last updated on 04/Feb/17

l o g 3^{2 x} = l o g 18 x

2 x l o g 3 = l o g 18 + l o g x

l o g x = y

0.95 x = 1.26 + y

x = \frac{1.26 + y}{0.95}

Facebook Tweet Pin