find the value of p given that 3^p × 3^(−1) × 5 × 3^(p−1) = 2 × 3^4


Question and Answers Forum

All Questions Topic List
Others Questions
Previous in All Question Next in All Question
Previous in Others Next in Others
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
$3^p × 3^(−1) × 5 × 3^(p−1) = 2 × 3^4 3^(p−1+p−1) ×5=2×3^4 3^(2p−6) =(2/5) log(3^(2p−6) )=log((2/5)) (2p−6)log 3=log 2−log 5 2p−6=((log 2−log 5)/(log 3)) p=(1/2){((log 2−log 5)/(log 3))+6} p=(1/2){((log 2−log 5+6log 3)/(log 3))} p=((log 2−log 5+6log 3)/(2log 3)) p=((log 2−log 5+log 3^6 )/(log 3^2 )) p=((log(2×3^6 ÷5))/(log 9))=((log(((1458)/5)))/(log 9))≈2.5830$
$3^{p} \times 3^{- 1} \times 5 \times 3^{p - 1} = 2 \times 3^{4}$ $3^{p - 1 + p - 1} \times 5 = 2 \times 3^{4}$ $3^{2 p - 6} = \frac{2}{5}$ $\log (3^{2 p - 6}) = \log (\frac{2}{5})$ $(2 p - 6) \log 3 = \log 2 - \log 5$ $2 p - 6 = \frac{\log 2 - \log 5}{\log 3}$ $p = \frac{1}{2} {\frac{\log 2 - \log 5}{\log 3} + 6}$ $p = \frac{1}{2} {\frac{\log 2 - \log 5 + 6 \log 3}{\log 3}}$ $p = \frac{\log 2 - \log 5 + 6 \log 3}{2 \log 3}$ $p = \frac{\log 2 - \log 5 + \log 3^{6}}{\log 3^{2}}$ $p = \frac{\log (2 \times 3^{6} \div 5)}{\log 9} = \frac{\log (\frac{1458}{5})}{\log 9} \approx 2.5830$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum