Question

Să se rezolve ecuațiile. a,b,c

Answer 1

$\displaystyle \mathtt{a)log_4x=2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~C.E.~x\ \textgreater \ 0}~\\ \\ \mathtt{log_4x=log_416 }\\ \\ \mathtt{x=16}\\ \\ \mathtt{b)lg(x-1)=-1 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~C.E.~x-1\ \textgreater \ 0 \Rightarrow x\ \textgreater \ 1}\\ \\ \mathtt{lg(x-1)=lg \frac{1}{10} }\\ \\ \mathtt{x-1= \frac{1}{10} }\\ \\ \mathtt{10x-10=1}\\ \\ \mathtt{10x=1+10}\\ \\ \mathtt{10x=11}\\ \\ \mathtt{x= \frac{11}{10} }$
$\displaystyle \mathtt{c)log_{ \frac{1}{4} }(7x+1)=log_927~~~~~~~~~~~~~~~~~~~~~~~~~C.E.~7x+1\ \textgreater \ 0\Rightarrow x\ \textgreater \ - \frac{1}{7} }\\ \\ \mathtt{log_{2^{-2}}(7x+1)=log_{3^2}3^3}\\ \\ \mathtt{- \frac{1}{2}log_2(7x+1)= \frac{3}{2} }\\ \\ \mathtt{-log_2(7x+1)=3}\\ \\ \mathtt{log_2(7x+1)=-3}\\ \\ \mathtt{log_2(7x+1)=log_2 \frac{1}{8} }\\ \\ \mathtt{7x+1= \frac{1}{8} }\\ \\ \mathtt{56x+8=1 }\\ \\ \mathtt{56x=1-8}\\ \\ \mathtt{56x=-7}\\ \\ \mathtt{x=- \frac{7}{56} \Rightarrow x=- \frac{1}{8} }$