Question

Find the logarithm of : `1/16` to the base 4

Answer 1

Let log₄`1/16` = x

∴ 4^x = `1/16`

⇒ 4^x = `1/[ 4 xx 4 ]`

⇒ 4^x = ( 4 x 4 )^-1

⇒ 4^x = ( 4² )^-1

⇒ 4^x = 4^-2

⇒ x = - 2      ....[ If a^m = aⁿ ; then m = n ]

∴ log₄`1/16` = - 2