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Exponential Inequalities

Exponential Inequalities - Multiple Terms

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

{3} < x \leq {13}

{4} \leq x < {14}

{5} \leq x < {15}

{2} < x \leq {12}

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by Brilliant Staff

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

x < {4}+\log_{7} {3}

x < {4}+\log_{7} {11}

x < {-4}-\log_{7} {11}

x < {-4}-\log_{7} {3}

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by Brilliant Staff

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

{-8} < x < {-3}

{-6} < x < {-1}

{-7} < x < {-2}

{-9} < x < {0}

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by Brilliant Staff

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

x>0

x>1

x>\log 2

x>\log 3

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by Brilliant Staff

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

\sqrt[n]{{6}^{n-1}}

{6}

\sqrt[n]{{6}^{n+1}}

\sqrt[n+1]{{6}^{n}}

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by Brilliant Staff

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