Question

Sa se rezolve in R
a) 3(lg(x-1)-2)=lg5-lg(x-1)
b)log in baza 1/2 din x^2 -lg 4=log in baza 1/2 din x+lg25

Answer 1

[tex]aDVA:x\ \textgreater \ 1 \\ )3lg(x-1)-6=lg5-lg(x-1) \\ 4lg(x-1)=lg10^6+lg5 \\ (x-1)^4=5*10^6 \\ x-1= \sqrt[4]{5*10^6} \\ x=10 \sqrt[4]{500}+1 \\ b) log_{ \frac{1}{2} } x^{2} -lg4= log_{ \frac{1}{2} }x+lg25 \\ x\ \textgreater \ 0 \\ log_{ \frac{1}{2} } x^{2} - log_{ \frac{1}{2} }x=lg4+lg25 \\ log_{ \frac{1}{2} }x=lg100 \\ log_{ \frac{1}{2} }x=2 \\ x= \frac{1}{4} [/tex]