Logarithms and Their Properties

These flashcards cover key concepts, definitions, and properties related to logarithms and their calculations.

What does log base 10 represent?

The power to which the base 10 must be raised to obtain a given number.

What is the relationship between logarithms and indices?

Logarithms are the inverse operations of exponentiation.

What is the result of log₁₀(100)?

2, because 10² = 100.

Can you take the logarithm of a negative number?

No, logarithms are only defined for positive numbers.

What is the log value of 3 (log₁₀(3))?

Approximately 0.477, because 10^0.477 ≈ 3.

What is the application of logs in calculations?

They simplify multiplication and division to addition and subtraction.

What is the base of natural logarithms?

Base e.

What is Rule 1 of logarithms?

ln(x) + ln(y) = ln(xy).

What does changing the base of a logarithm involve?

Converting a logarithm from one base to another.

What does log₁₀(398107.17) equal?

5.6.

What is the graphical behavior of the logarithmic function?

The graph grows slowly, even slower than y=x.

What is ln(1)?

0.

What is Rule 2 of logarithms?

ln(x) - ln(y) = ln(x/y).

What is Rule 3 of logarithms?

a ln(x) = ln(x^a).