Question

1/2logx+3log√x+2 = log√x(x+2) +2 ?

Answer 1

Bom dia

$\frac{1}{2}logx+3log \sqrt{x+2} =log \sqrt{x(x+2)} +2 \\ \\ log x^{ \frac{1}{2} } +log ( \sqrt{x+2} )^{3} =log \sqrt{x(x+2)} +log100 \\ \\ log \sqrt{x} } +log ( \sqrt{x+2} )^{3} =log \sqrt{x(x+2)} +log100 \\ \\ log[ \sqrt{x} * ( \sqrt{x+2} )^{3}]=log[100* \sqrt{x(x+2)} ] \\ \sqrt{x} * ( \sqrt{x+2} )^{3} =100* \sqrt{x*(x+2)}$

$\sqrt{x} * ( \sqrt{x+2} )^{2} * \sqrt{x+2} =100* \sqrt{x} * \sqrt{x+2} \\ \\  [tex] ( \sqrt{x+2} )^{2} =100\Rightarrow x+2=100\Rightarrow x=98$