I came across a problem and noticed that (ln4)/2 = ln√4. How do I rewrite (ln4)/2 into ln√4 or verify that the two are equal without a calculator?

Answer 1

ln [ nth root ( x ) ] = ln ( x ) / n

ln √4 = ln ( 4 ) / 2

OR

ln [ x ^ n )= n * ln ( x )

√4 = 4 ^ ( 1 / 2 )

ln [ 4 ^ ( 1 / 2 ) ] = ( 1 / 2 ) * ln ( 4 ) = ln ( 4 ) / 2