Question

Find the logarithm of : 0.125 to the base 2

Answer 1

Let log₂0.125 = x
∴ 2^x = 0.125
⇒ 2^x = `125/1000`
⇒ 2^x = `1/8`
⇒ 2^x = 8^-1
⇒ 2^x = ( 2 x 2 x 2 )^-1
⇒ 2^x = ( 2³ )^-1
⇒ 2^x = 2^-3
⇒ x = - 3     .....[ If a^m = aⁿ ; then m = n ]
∴ log₂0.125 = -3