# Logarithm-11

### From Homeworkwiki

**If log _{10} 2 = a; log_{10} 3 = b, what is the value of log_{5} 12?**

**Solution:** log_{5} 12 = log_{10} 12 / log_{10} 5

= log_{10} 12 / log_{10} (10 / 2) = log_{10} 12 / [log_{10} 10 - log_{10} 2]

= [log_{10} (2^{2} X 3)] / [1 - log_{10} 2] = [2 X log_{10} 2 + log_{10} 3] / [1 - log_{10} 2]

= (2a + b) / (1 - a)