How do you solve the equation $$log_b(x) = y$$ ?

To solve $$log_b(x) = y$$ , rewrite it in exponential form: $$x = b^y$$ .

How do you solve $$log_2(x) + log_2(x + 5) = log_2(3x + 8)$$ ?

Combine the logs: $$log_2(x(x + 5)) = log_2(3x + 8)$$ , then set the arguments equal: $$x(x + 5) = 3x + 8$$ . Solve for $$x$$ .

What is the solution to the equation $$7^{(3x+4)}=49^{(2x+1)}$$ ?

Rewrite $$49$$ as $$7^2$$ : $$7^{(3x+4)} = (7^2)^{(2x+1)}$$ . This simplifies to $$7^{(3x+4)} = 7^{(4x+2)}$$ . Set the exponents equal: $$3x + 4 = 4x + 2$$ , leading to $$x = 2$$ .

How do you solve $$3^{(2x - 6)} = 81$$ ?

Rewrite $$81$$ as $$3^4$$ : $$3^{(2x - 6)} = 3^4$$ . Set the exponents equal: $$2x - 6 = 4$$ , leading to $$x = 5$$ .

What is the solution to $$log_2(x + 3) = 4$$ ?

Rewrite in exponential form: $$x + 3 = 2^4$$ , which simplifies to $$x + 3 = 16$$ . Thus, $$x = 13$$ .

How do you solve the equation $$2^{(x-5)} + 6 = 30$$ ?

Subtract 6 from both sides: $$2^{(x-5)} = 24$$ . Then take the logarithm: $$x - 5 = log_2(24)$$ , leading to $$x = log_2(24) + 5$$ , which approximates to $$x = 9.58$$ .

What is the definition of an exponential function?

An exponential function is a mathematical function of the form $$f(x) = a \times b^x$$ , where $$a$$ is a constant, $$b$$ is a positive real number, and @@b eq 1@@.

What is the relationship between exponential and logarithmic functions?

Exponential functions and logarithmic functions are inverses of each other. If $$y = b^x$$ , then $$x = log_b(y)$$ .

What is the base of a logarithm?

The base of a logarithm is the number that is raised to a power to obtain a certain value. In $$log_b(a)$$ , $$b$$ is the base.

Solving Exponential and Logarithmic Equations Flashcards

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14 questions

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1.

FLASHCARD QUESTION

Front

What is the definition of a logarithm?

Back

2.

FLASHCARD QUESTION

Front

What is the change of base formula for logarithms?

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3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

What is the product property of logarithms?

Back

5.

FLASHCARD QUESTION

Front

What is the quotient property of logarithms?

Back

6.

FLASHCARD QUESTION

Front

What is the power property of logarithms?

Back

7.

FLASHCARD QUESTION

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