Algebra

Exponential Inequalities

Exponential Inequalities - Multiple Terms

         

Solve the following for x:x: {3x>93x2274x.\left\{\begin{matrix} 3^x > 9 \\ 3^{x^2} \leq 27^{4x}. \end{matrix}\right.

What is the range of xx that satisfies the inequality (149)x+4+(17)x+4>12? \left ( \frac{1}{49} \right )^{x+4} + \left ( \frac{1}{7} \right )^{x+4} > 12 ?

What is the range of xx that satisfies the inequality (15)3+x<625<(125)x? \left(\frac{1}{5}\right)^{3+x} < 625 < \left( \frac{1}{25} \right)^x ?

Given log2=0.3010\log 2=0.3010 and log3=0.4771,\log 3=0.4771, solve the inequality (27)x<(3x)6.\left(2 ^{7}\right)^x<\left(3 ^x\right)^{6}.

Given n2,n \geq 2, which of the following numbers is the largest: 6n1n,6n+1n,6nn+1,6? \sqrt[n]{6^{n-1}}, \sqrt[n]{6^{n+1}}, \sqrt[n+1]{6^n},6 ?

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