# Simplify logarithmic expression?

• Oct 8th 2009, 11:52 AM
tsmith
Simplify logarithmic expression?
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?
• Oct 8th 2009, 12:27 PM
Soroban
Hello, tsmith!

Quote:

Simplify: . $\log_{10}\left(\frac{9}{300}\right)$

$\log_{10}\left(\frac{9}{300}\right) \;=\;\log_{10}\left(\frac{3}{100}\right)$

. . . . . . . . $= \;\log_{10}(3) - \log_{10}(100)$

. . . . . . . . $= \;\log_{10}(3) - \log_{10}(10^2)
$

. . . . . . . . $-\; \log_{10}(3) - 2\cdot\underbrace{\log_{10}(10)}_{\text{This is 1}}$

. . . . . . . . $=\; \log_{10}(3) - 2$

• Oct 8th 2009, 12:36 PM
tsmith
Thank you so much! I understand it completely now.
(Rofl)