Exponential Inequalities: Problems with Solutions

By Denitsa Dimitrova (Bulgaria)
Problem 1
$5^{x^2+3} \le 5^{4x}$
Problem 2
$3^{\frac {x-3}{3x-2}} \le 3$
Problem 3
$\left(\frac{3}{4} \right)^{2-x} > \left(\frac{3}{4} \right)^{-\frac{1}{2}}$
Problem 4
$\left(\frac {1}{3} \right)^{2x^2-5} < \left(\frac {1}{9} \right)^{\frac {3}{2}}$
Problem 5
${0.4}^{3x-1} \ge {0.4}^{x+1}$
Problem 6
${5}^{x^2-6x+8} < 1$
Problem 7
$\left( \frac {3}{7} \right)^{\frac {x^2-2x}{x^2}} \ge 1$
Problem 8
$9^{x}-3^{x+1}+2 > 0$
Problem 9
$4^{x-1} \le 2^{x-2}+3$
Problem 10
$2^{x+1} + 2^{2-x} > 9$

Problem 11
$2^{x} + 2^{1-x} < 3$
Problem 12
$6^{2x+3} < 6^{x+7} \cdot 3^{2x-8}$
Problem 13
$2^{2x} - 2^{2+2\sqrt{x}} \le 3\cdot 2^{x+\sqrt{x}}$
Problem 14
$\left | 2^{4x^2-1} -5 \right | \le 3$
Problem 15
$3^{\left | x+2 \right |} + 3^{\left | x-1 \right |} \ge 28$
Problem 16
$3^{\left | x+3 \right |} - \left | 3^{x+2} -1 \right | < 3^{x+2} + 2$
Problem 17
$4^{2x} - 2 \cdot 4^{x} < 0$
Problem 18
$3\cdot 3^{2x} + 11 \cdot 3^{x} -4 > 0$
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