U4L3 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. For example, in the expression log_b(a) = c, b^c = a.

Front

What is the relationship between logarithms and exponents?

Back

Logarithms are the inverse operations of exponentiation. If b^c = a, then log_b(a) = c.

Front

What is the base of a logarithm?

Back

The base of a logarithm is the number that is raised to a power. In log_b(a), b is the base.

Front

Evaluate log_10(1000).

Back

3, because 10^3 = 1000.

Front

Convert the exponential equation 2^5 = 32 to logarithmic form.

Back

log_2(32) = 5.

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.

Front

Evaluate log_5(125).

Back

3, because 5^3 = 125.

Front

Convert log_3(81) = 4 to exponential form.

Back

3^4 = 81.

Front

What is the value of log_2(16)?

Back

4, because 2^4 = 16.

Front

Convert the logarithmic equation log_p(t) = m to exponential form.

Back

p^m = t.