Question

已知3的a次方=4的b次方=36,求2/a+1/b的值

已知3的a次方=4的b次方=36,求2/a+1/b的值

Answer 1

3^a=36
3^2a=36^2
9^a=36^2
所以9^ab=36^2b

4^b=36
4^ab=36^a

所以9^ab*4^ab=36^2b*36^a
36^(ab)=36^(2b+a)
所以2b+a=ab
两边除以ab
2/a+1/b=1

Answer 2

a=ln(36)/ln(3);b=ln(36)/ln(4);
2/a+1/b=2*ln(3)/ln(36)+ln(4)/ln(36)
=ln(9)/ln(36)+ln(4)/ln(36)
=[ln(9)+ln(4)]/ln(36)
=ln(9*4)/ln(36)
=1

Answer 3

1

Answer 4

2