Question

  mng giúp e với ạ, e cảm ơn ạ

c) \(\log_{\sqrt[4]{2}} \left( x^2 - 2 \right)^2 = 8\)

d) \(\log_2 \sqrt{x^2 + 5} = 3\)

Answer 1

c: \(log_{\sqrt[4]{2}}\left(x^2-2\right)^2=8\)

=>\(\left(x^2-2\right)^2=\left(\sqrt[4]{2}\right)^8=4\)

=>\(\left[{}\begin{matrix}x^2-2=2\\x^2-2=-2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x^2=4\\x^2=0\end{matrix}\right.\)

=>\(x\in\left\{2;-2;0\right\}\)

d: \(log_2\sqrt{x^2+5}=3\)

=>\(\sqrt{x^2+5}=2^3=8\)

=>\(x^2+5=8^2=64\)

=>\(x^2=59\)

=>\(x=\pm\sqrt{59}\)