Algebra II - Spring Final Exam

Front

What is a logarithm?

Back

A logarithm is the power to which a number (the base) must be raised to obtain another number. For example, if b^y = x, then log_b(x) = y.

Front

What is the natural logarithm?

Back

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

Front

Simplify: ln(e^3)

Back

3

Front

What is the value of ln(1)?

Back

0

Front

If log_b(x) = y, what is the equivalent exponential form?

Back

b^y = x

Front

What is the change of base formula for logarithms?

Back

log_b(a) = log_k(a) / log_k(b) for any base k.

Front

Simplify: log_10(1000)

Back

3

Front

What is the product rule for logarithms?

Back

log_b(xy) = log_b(x) + log_b(y) for any positive x and y.

Front

What is the quotient rule for logarithms?

Back

log_b(x/y) = log_b(x) - log_b(y) for any positive x and y.

Front

What is the power rule for logarithms?

Back

log_b(x^k) = k * log_b(x) for any positive x and real number k.