Giải thích các bước giải:
3,
TXĐ: \(D = \left( { - \infty ; + \infty } \right)\)
Ta có:
\[\begin{array}{l}
{3^{x - 2\sqrt 5 }} - 5 = 0\\
\Leftrightarrow {3^{x - 2\sqrt 5 }} = 5\\
\Leftrightarrow x - 2\sqrt 5 = {\log _3}5\\
\Leftrightarrow x = 2\sqrt 5 + {\log _3}5
\end{array}\]
4,
TXĐ: \(D = \left( { - \sqrt 7 ; + \infty } \right)\)
Ta có:\[\begin{array}{l}
\ln \left( {x + \sqrt 7 } \right) = 1\\
\Leftrightarrow x + \sqrt 7 = e\\
\Leftrightarrow x = e - \sqrt 7 \left( {t/m} \right)
\end{array}\]
5,
TXĐ: \(D = \left( { - \sqrt 2 ; + \infty } \right)\)
Ta có:
\[\begin{array}{l}
{\left( {\frac{1}{2}} \right)^{x + \sqrt 2 }} > \frac{1}{4}\\
\Leftrightarrow {\left( {\frac{1}{2}} \right)^{x + \sqrt 2 }} > {\left( {\frac{1}{2}} \right)^2}\\
\Leftrightarrow x + \sqrt 2 < 2\\
\Leftrightarrow x < 2 - \sqrt 2 \\
\Rightarrow - \sqrt 2 < x < 2 - \sqrt 2
\end{array}\]
