mathmath333
  • mathmath333
Logarithm question
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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mathmath333
  • mathmath333
\(\large \color{black}{\begin{align} &If \hspace{.33em}\\~\\ &\dfrac13 \log_{3}M+3\log_{3}N=1+\log_{0.008} 5 \hspace{.33em}\\~\\ &then \hspace{.33em}\\~\\ &(1)\ \ M^{9}=\dfrac{9}{N} \hspace{.33em}\\~\\ &(2)\ \ N^{9}=\dfrac{9}{M} \hspace{.33em}\\~\\ &(3)\ \ M^{3}=\dfrac{3}{N} \hspace{.33em}\\~\\ &(4)\ \ N^{9}=\dfrac{3}{M} \hspace{.33em}\\~\\ \end{align}}\)
perl
  • perl
\(\large \color{black} \\~\\ \dfrac13 \log_{3}M+3\log_{3}N=1+\log_{0.008} 5 \\~\\ \log_{3}M^{1/3}+\log_{3}N^3=1+\log_{0.008} 5 \\~\\ \log_{3}\left( M^{1/3}\cdot N^3\right)=1+\log_{0.008} 5 \\~\\ \log_{3}\left( M^{1/3}\cdot N^3\right)=1+\log_{1/125} 5 \\~\\ \log_{3}\left( M^{1/3}\cdot N^3\right)=1+(-1/3) \\~\\ \log_{3}\left( M^{1/3}\cdot N^3\right)=2/3 \\~\\ \left( M^{1/3}\cdot N^3\right)=3^{2/3} \\~\\ \left( M^{1/3}\cdot N^3\right)^3=\left(3^{2/3} \right)^3\\~\\ M\cdot N^9 = 3^2 \)
princeharryyy
  • princeharryyy
well there's another way to solve this question @mathmath333

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mathmath333
  • mathmath333
which one
princeharryyy
  • princeharryyy
the left side is easy to solve that yu would have done by the perls way.
princeharryyy
  • princeharryyy
for 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/ (0-log5)] which gives -1/3
princeharryyy
  • princeharryyy
@mathmath333
princeharryyy
  • princeharryyy
right*

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