Question

Determine o conjunto solução

Answer 1

$\begin{cases}x+y=240~~(i)\\ \log_{18}(x)-\log_{18}(y)=\log_{18}(11)~~(ii)\end{cases}\\\\\\ x=240-y~~em~~i:\\\\\\ \log_{18}(240-y)-\log(y)=\log_{18}(11)\\\\ \log_{18}\left( \dfrac{240-y}{y}\right)=\log_{18}(11)\\\\ \dfrac{240-y}{y}=11\\\\ 240-y=11\cdot y\\ 240-y=11y\\ 12y=240\\\\ y= \dfrac{240}{12}\\\\ \Large\boxed{y=20}\\\\ x+y=240\\ x+20=240\\\\ \Large\boxed{x=220}\\\\\\ \Large\boxed{\text{S}=\{(220,~20)\}}$