How do you solve the equation $$2^{3n}=4$$ ?

Convert 4 to a power of 2: $$2^{3n} = 2^2$$ . Therefore, $$3n = 2$$ , leading to $$n = \frac{2}{3}$$ .

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

Since the bases are the same, set the exponents equal: $$2x = -x$$ . Solving gives $$x = 0$$ .

How do you solve $$2(4)^{2x+1}=128$$ ?

First, rewrite 128 as $$2^7$$ . Then, express 4 as $$2^2$$ : $$2(2^2)^{2x+1} = 2^7$$ . This simplifies to $$2^{4x+3} = 2^7$$ , leading to $$4x + 3 = 7$$ , so $$x = 1$$ .

What is the solution to the equation $$(-3)^x=(-3)^{13}$$ ?

Since the bases are the same, set the exponents equal: $$x = 13$$ .

What is the logarithmic form of the exponential equation $$a^b = c$$ ?

The logarithmic form is $$\text{log}_a(c) = b$$ .

How do you convert an exponential equation to logarithmic form?

To convert $$a^b = c$$ to logarithmic form, write it as $$\text{log}_a(c) = b$$ .

What is the solution to the equation $$3^{x+1} = 9$$ ?

Rewrite 9 as $$3^2$$ . Therefore, $$x + 1 = 2$$ , leading to $$x = 1$$ .

What is the definition of a base in an exponential equation?

The base is the number that is raised to a power. In $$a^b$$ , $$a$$ is the base.

What is the definition of an exponent in an exponential equation?

The exponent indicates how many times the base is multiplied by itself. In $$a^b$$ , $$b$$ is the exponent.

How do you solve $$4^{x} = 16$$ ?

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

What is the solution to $$2^{x} = 32$$ ?

Rewrite 32 as $$2^5$$ . Therefore, $$x = 5$$ .

What is the importance of understanding exponential equations?

Exponential equations model real-world situations such as population growth, radioactive decay, and interest calculations.

Solving Exponential Equations Flashcard

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15 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

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

Back

7.

FLASHCARD QUESTION

Front

What is the first step in solving an exponential equation?

Back

Identify if the bases can be made the same or if logarithms need to be used.

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