Question

若2的x次方=4的（y+1）次方，3的（x-1）次方=27的y次方求xy的值

Answer 1

2^x=4^(y+1)
2^x=2^2(y+1)
所以x=2(y+1)
一试
3^(x-1)=27^y
3(x-1)=3^3y
所以（x-1）=3y
二试
联立求解上边一试
二试
y=1
x=4
xy=4
m^a=5
a=log(m)(5)
m^b=2
b=log(m)(2)
m^(3a+2b)=m^3a
*
m^2b=m^3log(m)(5)
*
m^2log(m)(2)
=m^log(m)(5)^3
*
m^log(m)(2)^2
=(5)^3
*(2)^2
=500