Simplify this logarithmic expression: log10(9/300)
My work:
log 10(9/300) = log10 9 - log10 300 = 0 - log10 9 (150 x 2) = ?
So am I doing this right? What is the next step?
Hello, tsmith!
Simplify: .$\displaystyle \log_{10}\left(\frac{9}{300}\right)$
$\displaystyle \log_{10}\left(\frac{9}{300}\right) \;=\;\log_{10}\left(\frac{3}{100}\right)$
. . . . . . . . $\displaystyle = \;\log_{10}(3) - \log_{10}(100)$
. . . . . . . . $\displaystyle = \;\log_{10}(3) - \log_{10}(10^2)
$
. . . . . . . . $\displaystyle -\; \log_{10}(3) - 2\cdot\underbrace{\log_{10}(10)}_{\text{This is 1}} $
. . . . . . . . $\displaystyle =\; \log_{10}(3) - 2 $