Question

解方程（有关对数）a^lgx * x^lga - 2(a^lgx + x^lga) + 3 = 0 x为未知数

Answer 1

lg(a^lgx)=lgx*lga

lg(x^lga)=lga*lgx

所以lg(a^lgx)=lg(x^lga)

设t=a^lgx,则原不等式变为

t*t-2(t+t)+3=0

t²-4t+3=0

解得,t=1或t=3

a^lgx=1,lgx=0,x=1

a^lgx=3,lgx=lg3/(lga),x=10^[lg3/(lga)]