Asked by Anonymous
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?
Answers
Answered by
Bosnian
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
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
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