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mathmath333
 one year ago
Logarithm question
mathmath333
 one year ago
Logarithm question

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mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0\(\large \color{black}{\begin{align} &If \hspace{.33em}\\~\\ &\dfrac13 \log_{3}M+3\log_{3}N=1+\log_{0.008} 5 \hspace{.33em}\\~\\ &then \hspace{.33em}\\~\\ &(1)\ \ M^{9}=\dfrac{9}{N} \hspace{.33em}\\~\\ &(2)\ \ N^{9}=\dfrac{9}{M} \hspace{.33em}\\~\\ &(3)\ \ M^{3}=\dfrac{3}{N} \hspace{.33em}\\~\\ &(4)\ \ N^{9}=\dfrac{3}{M} \hspace{.33em}\\~\\ \end{align}}\)

perl
 one year ago
Best ResponseYou've already chosen the best response.3\(\large \color{black} \\~\\ \dfrac13 \log_{3}M+3\log_{3}N=1+\log_{0.008} 5 \\~\\ \log_{3}M^{1/3}+\log_{3}N^3=1+\log_{0.008} 5 \\~\\ \log_{3}\left( M^{1/3}\cdot N^3\right)=1+\log_{0.008} 5 \\~\\ \log_{3}\left( M^{1/3}\cdot N^3\right)=1+\log_{1/125} 5 \\~\\ \log_{3}\left( M^{1/3}\cdot N^3\right)=1+(1/3) \\~\\ \log_{3}\left( M^{1/3}\cdot N^3\right)=2/3 \\~\\ \left( M^{1/3}\cdot N^3\right)=3^{2/3} \\~\\ \left( M^{1/3}\cdot N^3\right)^3=\left(3^{2/3} \right)^3\\~\\ M\cdot N^9 = 3^2 \)

princeharryyy
 one year ago
Best ResponseYou've already chosen the best response.0well there's another way to solve this question @mathmath333

princeharryyy
 one year ago
Best ResponseYou've already chosen the best response.0the left side is easy to solve that yu would have done by the perls way.

princeharryyy
 one year ago
Best ResponseYou've already chosen the best response.0for the write side log base(0.008) (5) you can write it as log base((0.2)^3) (5) which will equal to 1/3 * log base(0.2) 5 now 0.2 can be written as 1/5 that means 1/3 * [log base(1/5) 5] which in turns equals to 1/3 * [log 5/ (log(1/5))] which finally becomes 1/3 * [log 5/ (0log5)] which gives 1/3
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