Logarithms- Expand, Condense, Evaluate

Front

What does the letter 'k' represent in the general log function y = a*log_b(x-h)+k?

Back

The letter 'k' indicates the vertical shift of the function, telling us if the function has moved up or down.

Front

What does the letter 'a' represent in the general log function y = a*log_b(x-h)+k?

Back

The letter 'a' indicates the vertical stretch, compression, or reflection of the function.

Front

What is the change of base formula for logarithms?

Back

The change of base formula is log_b(a) = log_c(a) / log_c(b), where c is any positive number.

Front

What transformation does the function y = log(x+3) represent?

Back

The function y = log(x+3) represents a leftward shift of 3 units.

Front

How do you evaluate log_b(x) using a calculator?

Back

Use the change of base formula: log_b(x) = log(x) / log(b) using common or natural logarithms.

Front

What is the domain of the logarithmic function y = log_b(x)?

Back

The domain is x > 0, meaning the input must be positive.

Front

What is the range of the logarithmic function y = log_b(x)?

Back

The range is all real numbers, (-∞, ∞).

Front

What does it mean to condense logarithmic expressions?

Back

Condensing logarithmic expressions means to combine multiple logs into a single log using properties of logarithms.

Front

What is the product property of logarithms?

Back

The product property states that log_b(m*n) = log_b(m) + log_b(n).

Front

What is the quotient property of logarithms?

Back

The quotient property states that log_b(m/n) = log_b(m) - log_b(n).