(1)
(lg2)^2+lg2*lg50+lg25
=lg2(lg2+lg50)+lg25
=lg2lg100+2lg5
=2lg2+2lg5
=2(lg2+lg5)
=2lg10
=2
(2)
∵m=ln2
n=ln3
∴2m+3n
=2ln2+3ln3
=ln4+ln27
=ln108
∴e^(2m+3n)
=e^ln108
=108
(1)
(lg2)^2+lg2*lg50+lg25
=lg2(lg2+lg50)+lg25
=lg2lg100+2lg5
=2lg2+2lg5
=2(lg2+lg5)
=2lg10
=2
(2)
∵m=ln2
n=ln3
∴2m+3n
=2ln2+3ln3
=ln4+ln27
=ln108
∴e^(2m+3n)
=e^ln108
=108