# Logarithms-18

### From Homeworkwiki

**If log 2 = 0.3010 and log 3 = 0.4771 , find the value of :**

**(i) log 6 (ii) log 5 (iii) log √ 24**

**Solution :**

(i) **log 6** = log (2 X 3) = log 2 + log 3 = 0.3010 + 0.4771 = **0.7781**

(ii) **log 5** = log 10 / 2 = log 10 - log 2 = 1 - 0.3010 = **0.6990** [log 10 = 1]

(iii) **log √ 24** = log ( 24 ) ^{ 1 / 2 } = 1 / 2 log (2 ^{ 3 } X 3)

= 1 / 2 [3 X log 2 + log 3]

= 1 / 2 [3 X 0.3010 + 0.4771]

= **0.69005**