mathmath333
  • mathmath333
Logarithm question
Mathematics
chestercat
  • chestercat
See more answers at brainly.com
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this
and thousands of other questions

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

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

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
princeharryyy
  • princeharryyy
right*

Looking for something else?

Not the answer you are looking for? Search for more explanations.