I do.not have.the.answer.to this question, could.I.check.mine with yours?lg(75/16)-2lg(5/9)+lg(32/343), I got lg(486/343)...if I had gotten it wrong(most likely) could you please show me the working? Thankvyou so much
Hello, Tutu!
You gave us a problem with a typo . . .
Simplify: .log(75/16) - 2log(5/9) + log(32/243)
We have:
. . $\displaystyle \log\left(\frac{75}{16}\right) - \log\left(\frac{5}{9}\right)^2 + \log\left(\frac{32}{243}\right)$
. . . . $\displaystyle =\;\log\left(\frac{75}{16}\right) - \log\left(\frac{25}{81}\right) + \log\left(\frac{32}{243}\right)$
. . . . $\displaystyle =\;\log\left(\frac{75}{16} \div \frac{25}{81} \times \frac{32}{243}\right)$
. . . . $\displaystyle =\;\log\left(\frac{{\color{blue}\rlap{//}}75^3}{{\color{green}\rlap{//}}16}\cdot\frac{{\color{red}\rlap{//}}81}{{\color{blue}\rlap{//}}25}\cdot \frac{{\color{green}\rlap{//}}32^2}{{\color{red}\rlap{///}}243_3}\right) $
. . . . $\displaystyle =\;\log(2)$