greeneyes<3 Help me to condense an equation! Thanks! (: one year ago one year ago

1. greeneyes<3

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

2. satellite73

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

3. satellite73

then $3\log(2)=\log(2^3)=\log(8)$

4. satellite73

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

5. jim_thompson5910

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