Converting & Evaluating Logarithms & Exponential

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

Convert the logarithmic expression log_10(100) to exponential form.

Back

10^2 = 100.

Front

What is the value of log_2(8)?

Back

3, because 2^3 = 8.

Front

Convert the exponential expression 5^3 = 125 to logarithmic form.

Back

log_5(125) = 3.

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_3(27).

Back

3, because 3^3 = 27.

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

Convert log_4(16) to exponential form.

Back

4^2 = 16.

Front

What is the value of log_10(1)?

Back

0, because 10^0 = 1.