Question

a大于0,解关于x的方程1+log2真数（2lga—x）除以log2真数x=2logx真数2

Answer 1

1+log2真数（2lga—x）除以log2真数x=2logx真数2

logx(x)+log2[(2lga-x)]/log2(x)=logx(4)

logx(x)+logx(2lga-x)=logx(4)

logx[x(2lga-x)]=logx(4)

x(2lga-x)=4

x²-2lga*x+4=0

用求根公式解得

x=[2lga±根号(4(lga)²-16)]/2

=lga±根号((lga)²-4)

换底公式：loga(b)=logx(b)/logx(a),x是底数