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