Question

calcular o log(18x+10)-log(x+5)=1

Answer 1

Utilizando a propriedade do logaritmo do quociente, temos:

$log\,(18x+10)~-~log\,(x+5)~=~1\\\\\\log\,\left(\frac{18x+10}{x+5}\right)~=~1\\\\\\\frac{18x+10}{x+5}~=~10^1\\\\\\18x+10~=~(x+5)~.~10\\\\\\18x+10~=~10x+50\\\\\\18x-10x~=~50-10\\\\\\8x~=~40\\\\\\x~=~\frac{40}{8}\\\\\\\boxed{x~=~5}$