1/2lg(x-3)+lg根号4x+1=lg2+1/2lg3

lg(x-3)+lg(4x+1)=2lg2+lg3
(x-3)(4x+1)=12
4x²-11x-15=0
(4x-15)(x+1)=0
∴x=15/4 x=-1
检验：x=-1是增根
∴x=15/4是方程的解

(1/2)lg(x-3)+lg√(4x+1)=lg2+(1/2)lg3
lg( [(x-3)(4x+1)]^(1/2)) = lg(2√3)
(x-3)(4x+1) = 12
4x^2-11x-15=0
(4x-15)(x+1)=0
x=15/4 or -1 ( rejected)
ie
x= 15/4

1/2lg(x-3)+lg根号4x+1=lg2+1/2lg3
lg根号(x-3)+lg根号4x+1=lg2+lg根号3
lg√(x-3)√(4x+1)=lg2√3
√[(x-3)(4x+1)]=2√3
(√[(x-3)(4x+1)])²=(2√3)²
4x²-11x-3=12
4x²-11x-15=0
(4x-15)(x+1)=0
x=15/4
x=-1
经检验，x=-1是增根
∴x=15/4