x^lgx=5*2^(lgx^2-1)

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x^lgx=5*2^(lgx^2-1)

x^lgx=5*2^(lgx^2-1)
x^lgx=5*2^(lgx^2-1)

x^lgx=5*2^(lgx^2-1)
两边取对数,有:
lg(x^lgx)=lg(5*2^(lgx^2-1))
lgx*lgx=lg5+lg2^(lgx^2-1)
lgx^2=lg5+(lgx^2-1)*lg2
lgx^2=lg5+lg2lgx^2-lg2
(1-lg2)lgx^2=lg5-lg2
(lg10-lg2)lgx^2=lg(5/2)
lg5lgx^2=lg(5/2)
lgx^2=lg(5/2)/lg5
lgx^2=(1-lg2/lg5)
x^2=10^(1-lg2/lg5)
x=±√10^(1-lg2/lg5)

两边同时lg