Verified answer

log1000^1/2

= log (10)3/2

= 3/2 log10

=3/2 answer [log10 = 1]

log(1000) = log(10*10*10)

= log(10) + log(10) +log(10)

= 3*log(10) = 3*1 = 3

log(1000*^(1/2) = (1/2)*log(1000) = 1.5 <<<

log(1000)^(1/2) = (1/2) log(1000) = (1/2)3 = 1.5