All Flashcards

How does multiplying the input of a log function by a constant affect its graph?

Results in a vertical translation (shift up/down) of the graph.

How does raising the input of a log function to a power affect its graph?

Results in a vertical dilation (stretch or compression) of the graph.

How does changing the base of a logarithmic function affect its graph?

It affects the 'height' of the graph, as all log functions are vertical dilations of each other.

Explain the product property of logarithms.

The logarithm of a product is equal to the sum of the logarithms of the individual factors.

Explain the power property of logarithms.

The logarithm of a number raised to a power is equal to the power multiplied by the logarithm of the number.

Explain the change of base property of logarithms.

Allows you to convert a logarithm from one base to another, useful when calculators don't have the desired base.

Explain the relationship between logarithmic and exponential functions.

Logarithmic functions are the inverses of exponential functions. They 'undo' each other.

What is the product property of logarithms?

$\log_b(xy) = \log_b(x) + \log_b(y)$

What is the power property of logarithms?

$\log_b(x^n) = n\log_b(x)$

What is the change of base formula for logarithms?

$\log_b(x) = \frac{\log_a(x)}{\log_a(b)}$

How to express natural log in base e?

$\ln(x) = \log_e(x)$