Question

giải bpt:

\(2^{x+2}+5^{x+1}< 2^x+5^{x+2}\)

Answer 1

Lời giải:

$2^{x+2}+5^{x+1}< 2^x+5^{x+2}$
$\Leftrightarrow 2^{x+2}-2^x+5^{x+1}-5^{x+2}<0$

$\Leftrightarrow 2^x(2^2-1)+5^{x+1}(1-5)<0$

$\Leftrightarrow 3.2^x-4.5^{x+1}<0$

$\Leftrightarrow 3.2^x< 20.5^x$

$\Leftrightarrow (\frac{5}{2})^x> \frac{3}{20}$

$\Leftrightarrow x> \frac{\log(\frac{3}{20})}{\log(\frac{5}{2})}$