find-the-value-of-p-given-that-3-p-3-1-5-3-p-1-2-3-4-

Question Number 68617 by Rio Michael last updated on 14/Sep/19

f i n d t h e v a l u e o f p g i v e n t h a t

3^{p} \times 3^{- 1} \times 5 \times 3^{p - 1} = 2 \times 3^{4}

Commented by Rasheed.Sindhi last updated on 14/Sep/19

3^{p} \times 3^{- 1} \times 5 \times 3^{p - 1} = 2 \times 3^{4}

3^{p - 1 + p - 1} \times 5 = 2 \times 3^{4}

3^{2 p - 6} = \frac{2}{5}

\log (3^{2 p - 6}) = \log (\frac{2}{5})

(2 p - 6) \log 3 = \log 2 - \log 5

2 p - 6 = \frac{\log 2 - \log 5}{\log 3}

p = \frac{1}{2} {\frac{\log 2 - \log 5}{\log 3} + 6}

p = \frac{1}{2} {\frac{\log 2 - \log 5 + 6 \log 3}{\log 3}}

p = \frac{\log 2 - \log 5 + 6 \log 3}{2 \log 3}

p = \frac{\log 2 - \log 5 + \log 3^{6}}{\log 3^{2}}

p = \frac{\log (2 \times 3^{6} \div 5)}{\log 9} = \frac{\log (\frac{1458}{5})}{\log 9} \approx 2.5830