# Logarithms-16

### From Homeworkwiki

**Without using log tables, evaluate : 2 log _{ 10 } 5 + log _{ 10 } 8 - 1 / 2 log _{ 10 } 4**

**Solution:**

**2 log _{ 10 } 5 + log _{ 10 } 8 - 1 / 2 log _{ 10 } 4**

= log _{ 10 } 5 ^{ 2 } + log _{ 10 } 8 - log _{ 10 } (4) ^{ 1 / 2 }

= log 25 + log 8 - log 2 [if no base is written, it means the base is 10]

= log [ (25 X 8) / 2 ] = log 100 = **2**

[log _{ 10 } 100 = 2]