F4B-F6 Review: Logs, exp, inverses and stuff

Front

What is a logarithm?

Back

A logarithm is the exponent to which a base must be raised to produce a given number. For example, log_b(a) = c means b^c = a.

Front

Evaluate log_3(1/3)

Back

-1

Front

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

Back

The domain is (0, ∞) because logarithms are only defined for positive real numbers.

Front

Evaluate log_4(1)

Back

0

Front

What is the value of log_b(b)?

Back

1, because any number raised to the power of 1 is itself.

Front

Evaluate log_12(1)

Back

0

Front

If log_x(25) = 2, what is x?

Back

5, because x^2 = 25.

Front

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

Back

The range is (-∞, ∞) because logarithmic functions can take any real value.

Front

What is the change of base formula for logarithms?

Back

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

Front

Evaluate log_10(1000)

Back

3, because 10^3 = 1000.