# Logarithms-15

### From Homeworkwiki

**Express as a single logarithm :**

**2 + 1 / 2 log _{10} 9 - 2 log _{10} 5**

**Solution:**

**2 + 1 / 2 log _{10} 9 - 2 log _{10} 5**

= log _{10} 100 + 1 / 2 log _{10} 3 ^{2} - log _{10} 5 ^{2} [log _{10} 100 = 2 ; log 9 = log 3 ^{2} and 2 log 5 = log 5^{2}]

= log _{10} 100 + 1 / 2 X 2 log _{10} 3 - log _{10} 25

= log _{10} (100 X 3) / 25 = **log _{10} 12** [log a + log b - log c = log { [ (a X b) / c] }