# Logarithms-17

### From Homeworkwiki

**Find x , if : (i) log _{ 10 } (x + 5) = 1**

**(ii) log _{ 10 } (x + 1) + log _{ 10 } (x - 1) = log _{ 10 } 11 + 2 log _{ 10 } 3**

**Solution:**

(i) log _{ 10 } (x + 5) = 1 = log _{ 10 } 10

=> (x + 5) = 10

=> **x = 5**

(ii)log _{ 10 } (x + 1) + log _{ 10 } (x - 1) = log _{ 10 } 11 + 2 log _{ 10 } 3

=> log _{ 10 } (x + 1) (x - 1) = log _{ 10 } 11 + log _{ 10 } 3 ^{ 2 }

=> log (x ^{2} - 1) = log (11 X 9)

=> x ^{ 2 } - 1 = 99

Therefore, x ^{ 2 } = 100

**=> x = 10**