Question

27^x=67 81^y=603 求证：4y-3x-2=2

Answer 1

方法1：
27^x=67 3^3x=67
81^y=603 3^4y=603
603/67
=3^4y/3^3x
=3^(4y-3x)
=9=3^2
4y-3x=2

方法2：27^x=67 x=log(27)67
3x=3log(27)67
=3log(3^3)67
=log(3)67
81^y=603 y=log(81)603
4y=4log(81)603
=4log(3^4)603
=log(3)603
4y-3x
=log(3)603-log(3)67
=log(3)(603/67)
=log(3)9
=2 所以4y-3x=2