# Logarithms-14

### From Homeworkwiki

**Express log _{10} 108 ^{1 / 5 } in terms of log _{10} 2 and log _{10} 3.**

**Solution:**

log _{10} 108 ^{1 / 5 } = 1 / 5 log _{10} 108 [log _{10} n ^{m} = m log _{ 10} n]

= 1 / 5 log _{10} (2 ^{2} X 3 ^{3}) [ 108 = 2 X 2 X 3 X 3 X 3 = 2 ^{2} X 3 ^{3} ]

= 1 / 5 [log _{10} 2 ^{2}+ log _{10} 3 ^{3}] [log _{10} (m X n) = log _{10} m + log _{10} n]

= ** 1 / 5 [2 log _{10} 2 + 3 log _{10} 3]**