What does it mean if $$a^x > a^y$$ ?

If $$a^x > a^y$$ and the base a is greater than 1, then it implies that $$x > y$$ . If the base a is between 0 and 1, then it implies that $$x

Solve the inequality: $$10^{4x+1} > 100^{x-2}$$

The solution is $$x > -\frac{5}{2}$$ .

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

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

What is the logarithmic form of an exponential equation?

The logarithmic form of an exponential equation $$a^b = c$$ is $$\text{log}_a(c) = b$$ .

What is the property of exponents that states $$a^{m+n} = a^m \times a^n$$ ?

This is known as the Product of Powers Property.

What is the property of exponents that states $$\frac{a^m}{a^n} = a^{m-n}$$ ?

This is known as the Quotient of Powers Property.

What is the property of exponents that states $$(a^m)^n = a^{mn}$$ ?

This is known as the Power of a Power Property.

What is the relationship between exponential functions and their graphs?

Exponential functions have a characteristic curve that increases or decreases rapidly, depending on the base, and they never touch the x-axis (asymptotic behavior).

6.2 Solving Exponential Inequalities Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is an exponential inequality?

Back

2.

FLASHCARD QUESTION

Front

How do you solve exponential inequalities?

Back

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.

3.

FLASHCARD QUESTION

Front

What is the base of an exponential function?

Back

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