Question

Find the logarithm of : 27 to the base 9

Answer 1

Let log₉27 = x
∴ 9^x = 27
⇒ ( 3 x 3 )^x = 3 x 3 x 3
⇒ (3²)^x = 3³
⇒ (3²)^x = 3³
⇒ 2x = 3         .....[ If a^m = aⁿ ; then m = n ]
⇒ x = `3/2`
∴ log₉27 = `3/2`