Question

已知3的x次方等于4,3的y次方等于6，求9的2x-y次方加27的x-y次方的值

Answer 1

设3的x次方是4，则
3＾x=4
<==> lg3^x=lg4
<==> xlg3=2lg2
<==> x=(2lg2)/lg3
<==> x=(2*0.3010)/0.4771
<==> x=1.26次方．
3^x=6

log3(6)=x

解出x=1.6309
9^2×1.26-1.6309+27^1.26-1.6309 具体多少楼主自己算吧

Answer 2

9^(2x-y)+27^(x-y)
=3^2(2x-y)+3^3(x-y)
=3^(4x-2y)+3^(3x-3y)
=(3^4x)/(3^2y)+(3^3x)/(3^3y)

3^x=4
3^4x=(3^x)^4=4^4=256
3^3x=(3^x)^3=4^3=64

3^y=6
3^2y=(3^y)^2=6^2=36
3^3y=(3^y)^3=6^3=216

原式=256/36+64/216=(1536+64)/216=200/27

Answer 3

9^(2x-y)+27^(x-y)=3^(4x-2y)+3^(3x-3y)=(3^x)^4/(3^y)^2+(3^x)3/(3^y)3=4^3/6^2+4^3/6^3=64/36+64/108=256/108=64/27