log以2为底2的x次方+1的对数乘以log以2为底2的x+1次方+2的对数=2解方程

令a=2^x+1
则2^(x+1)+2=2a
所以log2(a)*log2(2a)=2
log2(a)*[log2(2)+log2(a)]=2
[log2(a)]²+log2(a)-2=0
[log2(a)+2][log2(a)-1]=0
log2(a)=-2,log2(a)=1
a=1/4,a=2
2^x+1=1/4
2^x=-3/4