Question

Sa se rezolve ecuatiile :
lg(2x+6)-2lg(2x-3)=1
lg(x-5)+lg(x+4)=lg2+g5

Answer 1

[tex]a)x\ \textgreater \ - \frac{3}{2} \\ lg(2x+6)-2lg(2x+3)=1 \\ lg(2x+6)=lg10+lg(2x+3)^2 \\ 2x+6=10(4 x^{2} +12x+9) \\ 40 x^{2} +118x+84=0/:2 \\ 20 x^{2} +59x+42=0 \\ x_{1}= \frac{-59+11}{40}=- \frac{6}{5} ; x_{2}=- \frac{7}{4} \\ Raspuns:x=- \frac{6}{5} [/tex]
[tex]b) x\ \textgreater \ 5 \\ (x-5)(x+4)=10 \\ x^{2} -x-30=0 \\ x_{1}=-5; x_{2}=6 \\ Raspuns:x=6[/tex]