Question

Find the logarithm of : `1/81` to the base 27

Answer 1

Let log₂₇`1/81` = x

∴ 27^x = `1/81`

⇒ ( 3 x 3 x 3 )^x = `1/( 3 xx 3 xx 3 xx 3 )`

⇒  (3³)^x = `1/(3^4)`

⇒  (3³)^x = (3⁴)^-1

⇒  3^3x = 3^-4

⇒ 3x = - 4           .....[ If a^m = aⁿ ; then m = n ] 

⇒ x = `-4/3`

∴ log₂₇`1/81 = - 4/3`