What is the natural logarithm?

The natural logarithm is the logarithm to the base e, where e is approximately equal to 2.71828. It is denoted as $$\text{ln}(x)$$ .

How do you apply logarithmic properties to simplify expressions?

Logarithmic properties include: 1) $$\text{log}_a(xy) = \text{log}_a(x) + \text{log}_a(y)$$ , 2) $$\text{log}_aigg(\frac{x}{y}igg) = \text{log}_a(x) - \text{log}_a(y)$$ , and 3) $$\text{log}_a(x^n) = n \times \text{log}_a(x)$$ .

What is the base of a logarithm?

The base of a logarithm is the number that is raised to a power to obtain a given number. For example, in $$\text{log}_2(8)$$ , the base is 2.

What is the relationship between exponential and logarithmic functions?

Exponential functions and logarithmic functions are inverses of each other. If $$y = a^x$$ , then $$x = \text{log}_a(y)$$ .

How do you isolate the variable in an exponential equation?

To isolate the variable in an exponential equation, you can use logarithms to bring the exponent down, allowing you to solve for the variable.

What is the significance of the number e in exponential equations?

The number e is the base of natural logarithms and is significant in continuous growth or decay processes, often appearing in equations involving exponential growth.

Solving Exponential Equations Using Logs Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is an exponential equation?

Back

2.

FLASHCARD QUESTION

Front

How do you solve an exponential equation using logarithms?

Back

3.

FLASHCARD QUESTION

Front

What is the definition of a logarithm?

Back

Tags

CCSS.HSF.BF.B.5

4.

FLASHCARD QUESTION

Front

What is the change of base formula for logarithms?

Back

5.

FLASHCARD QUESTION

Front

How do you round a number to three decimal places?

Back

To round a number to three decimal places, look at the fourth decimal place. If it is 5 or greater, round up the third decimal place by one. If it is less than 5, keep the third decimal place the same.

Tags

CCSS.5.NBT.A.4

6.

FLASHCARD QUESTION

Front

Back

x = -2.54.

Tags

CCSS.HSF.LE.A.4

7.

FLASHCARD QUESTION

Front

Back

x = -1.42.

Tags

CCSS.HSF.LE.A.4

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