Question

Ecuații logaritmice. Să se rezolve ecuațiile :
a) lg(x-1)=-1
b) log de x+1 în baza 5=1

Answer 1

   
[tex]\displaystyle \\ a)\\ \lg(x-1)= -1 \\ \\ x-1=10^{-1} \\ \\ x-1 = \frac{1}{10} ~~~\Big| ~\cdot 10 \\ \\ 10(x-1)=1\\\\ 10x-10=1 \\ \\ 5x = 1+10 \\ \\ 5x = 11 \\ \\ x= \boxed{\frac{11}{5}} \\ \\ \\ b) \\ \log_5 (x+1) =1 \\ \\ x+1 = 5^1 \\ \\ x+1 = 5 \\ \\ x = 5-1 = \boxed{4}[/tex]

Answer 2

$\displaystyle a)lg(x-1)=-1 ~~~~~~~~~~~~~~~~~~~C.E.~x-1\ \textgreater \ 0 \Leftrightarrow x\ \textgreater \ 1 \\ \\lg(x-1)=lg \frac{1}{10} \\ \\ x-1= \frac{1}{10} \\ \\ x= \frac{1}{10} +1 \\ \\ \boxed{x= \frac{11}{10} } \\ \\ b)log_5(x+1)=1~~~~~~~~~~~~~~~~~~~C.E.~x+1\ \textgreater \ 0 \Leftrightarrow x\ \textgreater \ -1\\ \\ log_5(x+1)=log_55 \\ \\ x+1=5 \\ \\ x=5-1 \\ \\ \boxed{x=4}$