# Logarithms-13

### From Homeworkwiki

**Find x, if : (i) log _{2} x = - 2**

**(ii) log _{4} (x + 3) = 2**

**(iii) log _{9} 27 = x**

**(iv) log _{x} 64 = 3 / 2**

**(v) log _{2} (x ^{2} - 4) = 5**

**Solution:**

(i) log _{2} x = - 2

=> 2 ^{-2} = x

**=> x = 1 / 4**

(ii) log _{4} (x + 3) = 2

=> 4 ^{2} = x + 3

=> **x** = 16 - 3 = **13**

(iii) log _{9} 27 = x

=> 9 ^{x} = 27

=> 3 ^{2x} = 3 ^{3}

=> **x = 3 / 2**

(iv) log _{x} 64 = 3 / 2

=> x ^{3 / 2} = 64

=> **x** = (64) ^{2 / 3 } = (2 ^{6}) ^{2 / 3 } = **16**

(v) log _{2} (x ^{2} - 4) = 5

=> 2 ^{5} = x ^{2} - 4

=> x ^{2} = 32 + 4 = 36

=> **x = ± 6**