Question

Giải các bất phương trình sau:

a) \({\left( {\frac{1}{3}} \right)^{2{\rm{x}} + 1}} \le 9\);

b) \({4^x} > {2^{x - 2}}\).

Answer 1

\(a,\left(\dfrac{1}{3}\right)^{2x+1}\le9\\ \Leftrightarrow2x+1\ge-2\\ \Leftrightarrow2x\ge-3\\ \Leftrightarrow x\ge-\dfrac{3}{2}\)

\(b,4^x>2^{x-2}\\ \Leftrightarrow2^{2x}>2^{x-2}\\ \Leftrightarrow2x>x-2\\ \Leftrightarrow x>-2\)