6.2 Solving Exponential Inequalities

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What is an exponential inequality?

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How do you solve exponential inequalities?

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To solve exponential inequalities, you can take the logarithm of both sides, use properties of exponents, or rewrite the inequality in a comparable form. Always consider the base of the exponent when determining the direction of the inequality.

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What is the base of an exponential function?

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What is the significance of the base in exponential inequalities?

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The base determines the direction of the inequality when comparing exponential expressions. A base greater than 1 maintains the inequality direction, while a base between 0 and 1 reverses it.

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Solve the inequality: @@10^{2x+7} geq 1000^x@@

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The solution is @@x geq 7@@.

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Solve the inequality: @@rac{1}{64}^{2x+3} leq 8^x@@

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The solution is @@x geq -rac{18}{15}@@.