Converting between Exponents and Logs

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, log_b(a) = c means b^c = a.

Front

Convert log_10(100) to exponential form.

Back

10^2 = 100.

Front

What is the base in a logarithmic expression?

Back

The base is the number that is raised to a power in a logarithmic expression, denoted as log_b(a), where b is the base.

Front

Convert log_5(25) to exponential form.

Back

5^2 = 25.

Front

What is the relationship between exponents and logarithms?

Back

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

Front

Convert log_4(16) to exponential form.

Back

4^2 = 16.

Front

What is the definition of the change of base formula?

Back

The change of base formula allows you to convert a logarithm to a different base: log_b(a) = log_k(a) / log_k(b) for any positive k.

Front

Convert log_2(32) to exponential form.

Back

2^5 = 32.

Front

What does log_b(1) equal?

Back

log_b(1) = 0 for any base b > 0.

Front

Convert log_7(49) to exponential form.

Back

7^2 = 49.