How do you solve the equation $$2^x = 16$$ ?

Rewrite 16 as $$2^4$$ , so $$x = 4$$ .

How do you solve $$3^{(x+1)} = 27$$ ?

Rewrite 27 as $$3^3$$ , so $$x + 1 = 3$$ , thus $$x = 2$$ .

What is the solution to the equation $$3^{26} = 3^{(4x + 2)}$$ ?

Since the bases are the same, set the exponents equal: $$26 = 4x + 2$$ , solving gives $$x = 6$$ .

What does it mean to rewrite an equation in exponential form?

It means expressing the equation such that the variable is in the exponent, allowing for easier manipulation.

What is the property of exponents that allows you to set exponents equal when bases are the same?

This property states that if $$a^m = a^n$$ , then $$m = n$$ .

How do you solve $$4^x = 64$$ ?

Rewrite 64 as $$4^3$$ , so $$x = 3$$ .

What is the solution to $$5^{2x} = 25$$ ?

Rewrite 25 as $$5^2$$ , so $$2x = 2$$ , thus $$x = 1$$ .

How do you solve $$10^x = 0.01$$ ?

Rewrite 0.01 as $$10^{-2}$$ , so $$x = -2$$ .

What is the solution to $$7^{x-1} = 49$$ ?

Rewrite 49 as $$7^2$$ , so $$x - 1 = 2$$ , thus $$x = 3$$ .

What is the significance of the base in an exponential equation?

The base determines the growth rate of the exponential function.

How do you approach solving $$e^{x} = 20$$ ?

Take the natural logarithm of both sides: $$x = \text{ln}(20)$$ .

What is the general form of an exponential function?

The general form is $$f(x) = a \times b^x$$ , where $$a$$ is a constant and $$b$$ is the base.

Solve Exponential Equations by Rewriting the Base Flashcards

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16 questions

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1.

FLASHCARD QUESTION

Front

What is an exponential equation?

Back

2.

FLASHCARD QUESTION

Front

Back

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

How can you express 36 as a power of 6?

Back

7.

FLASHCARD QUESTION

Front

What is the first step in solving an exponential equation?

Back

Identify if both sides can be expressed with the same base.

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