Question

Help me to condense an equation! Thanks! (:

Answer 1

\[3(\log_{3}14-\log_{3}7)+ 2 \log_{3}5\]

Answer 2

\[\log(14)-\log(7)=\log(\frac{14}{7})=\log(2)\] is a start

Answer 3

then
\[3\log(2)=\log(2^3)=\log(8)\]

Answer 4

and finally
\[\log(8)=2\log(5)\log(8)+\log(5^2)=\log(8\times 25)=\log(200)\]

Answer 5

Made a typo, but I fixed it


\[\Large 3\left(\log_{3}(14)-\log_{3}(7)\right)+ 2 \log_{3}(5)\]


\[\Large 3\log_{3}\left(\frac{14}{7}\right)+ 2 \log_{3}(5)\]


\[\Large 3\log_{3}\left(2\right)+ 2 \log_{3}(5)\]


\[\Large \log_{3}\left(2^3\right)+ \log_{3}(5^2)\]


\[\Large \log_{3}\left(8\right)+ \log_{3}(25)\]


\[\Large \log_{3}(8*25)\]


\[\Large \log_{3}(200)\]


So \[\Large 3\left(\log_{3}(14)-\log_{3}(7)\right)+ 2 \log_{3}(5)=\log_{3}(200)\]