1.（lg2)^2+lg2*lg50+lg252.已知ln2=m,ln3=n,求e^2m+3n

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1.（lg2)^2+lg2*lg50+lg252.已知ln2=m,ln3=n,求e^2m+3n

1.（lg2)^2+lg2*lg50+lg252.已知ln2=m,ln3=n,求e^2m+3n
1.（lg2)^2+lg2*lg50+lg25
2.已知ln2=m,ln3=n,求e^2m+3n

1.（lg2)^2+lg2*lg50+lg252.已知ln2=m,ln3=n,求e^2m+3n
(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=lg2*lg100+2lg5
=2lg2+2lg5=2lg10=2
2、ln2=m，所以e^m=2，同理e^n=3，
e^2m+3n=(e^m)^2*(e^n)^3=2^2*3^3=4*27=108

(1)2.(2)6.

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