作业帮x1满足2x+2^x=5,x2满足2x+2log2(x-1)=5,x1+x2=?
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x1满足2x+2^x=5,x2满足2x+2log2(x-1)=5,x1+x2=?
x1满足2x+2^x=5,x2满足2x+2log2(x-1)=5,x1+x2=?
x1满足2x+2^x=5,x2满足2x+2log2(x-1)=5,x1+x2=?
令log2(x2-1)=t
∴x2=2^t+1
∴2(2^t+1)+2t=5
∴2^(t+1)+2(t+1)=5
∴t+1=x1
∴x1+x2
=t+1+2^t+1
=[2^(t+1)+2(t+1)]/2+1
=5/2+1
=7/2
2x+2^x=5
x+2^(x-1)=2.5
2x+2log2(x-1)=5
x+log2(x-1)=2.5
其中y=2^(x-1)与y=log2(x-1)关于y=x-1对称
y=2.5-x与前面指数,对数曲线交点即为x1,x2.
x1+x2为y=2.5-x,y=x-1交点横坐标2倍即3.5
参考图片
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