6-x-2-2-3-x-find-x-

Question Number 22345 by ibraheem160 last updated on 16/Oct/17

6^{x + 2} = 2 (3^{x}), find x ?

Commented by JI Siam last updated on 21/Dec/17

Here 6^{x + 1} = 3^{x - 1} so, likely x is not a normal number .

Answered by $@ty@m last updated on 16/Oct/17

3^{x + 2} . 2^{x + 2} = 2 . 3^{x}

\frac{3^{x + 2}}{3^{x}} = \frac{2}{2^{x + 2}}

3^{2} = \frac{1}{2^{x + 1}}

2^{x + 1} = \frac{1}{3^{2}}

\log 2^{x + 1} = \log \frac{1}{3^{2}}

(x + 1) \log 2 = \log 1 - \log 3^{2}

(x + 1) \log 2 = - 2 \log 3

x + 1 = \frac{- 2 \log 3}{\log 2}

x = \frac{- 2 \log 3}{\log 2} - 1

Commented by $@ty@m last updated on 16/Oct/17

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