What is the value of $$\log_10(1000)$$ ?

$$3$$ , because $$10^3 = 1000$$ .

What is the relationship between exponential and logarithmic functions?

Exponential functions are the inverse of logarithmic functions.

What is the base of natural logarithms?

The base of natural logarithms is $$e$$ , where $$e \approx 2.718$$ .

Exponential and Logarithmic Equations Flashcard: 15 Cards

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15 questions

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1.

FLASHCARD QUESTION

Front

Convert the exponential equation $3^x = 81$ to its logarithmic form.

Back

$\log_3(81) = x$ .

2.

FLASHCARD QUESTION

Front

Solve the logarithmic equation: $\log_2(x) = 5$ .

Back

$x = 32$ .

3.

FLASHCARD QUESTION

Front

Solve the exponential equation: $2^{x+1} = 16$ .

Back

$x = 3$ .

4.

FLASHCARD QUESTION

Front

Solve for 'x': $\log_6(3x - 2) = \log_6(5x - 8)$ .

Back

$x = 3$ .

5.

FLASHCARD QUESTION

Front

Simplify: $\log_5(25) + \log_5(5)$ .

Back

$\log_5(125)$ .

6.

FLASHCARD QUESTION

Front

What is the definition of a logarithm?

Back

A logarithm is the exponent to which a base must be raised to produce a given number.

7.

FLASHCARD QUESTION

Front

What is the change of base formula for logarithms?

Back

$\log_b(a) = \frac{\log_k(a)}{\log_k(b)}$ for any base $k$ .

8.

FLASHCARD QUESTION

Front

What is the product property of logarithms?

Back

$\log_b(mn) = \log_b(m) + \log_b(n)$ .

9.

FLASHCARD QUESTION

Front

What is the quotient property of logarithms?

Back

$\log_b(\frac{m}{n}) = \log_b(m) - \log_b(n)$ .

10.

FLASHCARD QUESTION

Front

What is the power property of logarithms?

Back

$\log_b(m^p) = p \cdot \log_b(m)$ .

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