evaluate logarithms

Front

What is the definition of a logarithm?

Back

A logarithm is the exponent to which a base must be raised to produce a given number.

Front

What is the relationship between logarithmic and exponential forms?

Back

If log_b(a) = c, then it can be rewritten in exponential form as b^c = a.

Front

Evaluate log_4(16). What is the answer?

Back

2, because 4^2 = 16.

Front

Rewrite log_p(t) = m in exponential form.

Back

p^m = t.

Front

Rewrite log_2(8) = 3 in exponential form.

Back

2^3 = 8.

Front

What is the logarithmic form of the equation 3^4 = 81?

Back

log_3(81) = 4.

Front

Convert the equation 6^2 = 36 into logarithmic form.

Back

log_6(36) = 2.

Front

What is the base of a logarithm?

Back

The base of a logarithm is the number that is raised to a power to obtain a certain value.

Front

How do you evaluate log_b(b)?

Back

log_b(b) = 1, because any number raised to the power of 1 is itself.

Front

What is the change of base formula for logarithms?

Back

log_b(a) = log_k(a) / log_k(b), where k is any positive number.