(i)x=(ln7+3)/2...its easy. take ln both sides.

(ii)h(x)=2e^x-3

its minimum value will be when the term 2e^x is minimum since 3 is constant ..2e^x can attain a minimum zero(just attain) at x=-infinity.And its maximum value will be infinity.therefore range is (-3,infinity)

(iii)for finding h inverse take log again..

Hope it helps....