Question

Determine a condição de existência para:
a) log (2x + 6) na base 4.
b) log 64 na base x-2

Answer 1

$\boxed{\begin{array}{l}\rm a)~\rm\log_4(2x+6)\\\rm 2x+6>0\\\rm 2x>-6\\\rm x>-\dfrac{6}{2}\\\\\rm x>-3\\\rm b)~\log_{x-2}64\\\rm x-2>0\\\rm x>2\\\rm x-2\ne1\\\rm x\ne1+2\\\rm x\ne3\end{array}}$