Question

lg(x+9)-2=$\frac{1}{2}$lg(2x+3)-lg25

Answer 1

x>-3/2
lg(x+9)+lg25=1/2*lg(2x+3)+2
lg(x+9)+lg25=1/2*lg(2x+3)+lg100
aplicam proprietatile logaritmului
25(x+9)=100(√2x+3)
$x+9=4 \sqrt{2x+3} \\ x \geq -9 \\ x^{2} +18x+81=32x+48 \\ x^{2} -14x+33=0 \\ x_{1}=3; x_{2}=11$