log and exponential form

Front

What is the definition of 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 that b^c = a.

Front

What is the relationship between logarithmic and exponential forms?

Back

Logarithmic form expresses an exponent, while exponential form expresses the result of raising a base to an exponent. For example, log_b(a) = c is equivalent to b^c = a.

Front

Convert log₁₀(100) to exponential form.

Back

10² = 100.

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. In log_b(a), b is the base.

Front

How do you convert an exponential equation to logarithmic form?

Back

To convert an exponential equation of the form b^c = a to logarithmic form, write it as log_b(a) = c.

Front

What is the value of log_b(1) for any base b?

Back

The value of log_b(1) is always 0, because any number raised to the power of 0 equals 1.

Front

What is the value of log_b(b)?

Back

The value of log_b(b) is always 1, because any number raised to the power of 1 equals itself.

Front

How do you solve for x in the equation 2^x = 8?

Back

Convert to logarithmic form: x = log₂(8). Since 2³ = 8, x = 3.

Front

What is the change of base formula for logarithms?

Back

The change of base formula states that log_b(a) = log_k(a) / log_k(b) for any positive base k.

Front

Convert log₄(16) to exponential form.

Back

4² = 16.