Logarithmic Functions Practice

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. It is expressed as log_b(a) = c, meaning b^c = a.

Front

How do you convert a logarithmic equation to exponential form?

Back

To convert a logarithmic equation log_b(a) = c to exponential form, rewrite it as b^c = a.

Front

What is the value of log₁₀10?

Back

The value of log₁₀10 is 1.

Front

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

Back

The value of log_b(b) is always 1.

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

What is the common logarithm?

Back

The common logarithm is the logarithm with base 10, denoted as log(x) or log₁₀(x).

Front

What is the natural logarithm?

Back

The natural logarithm is the logarithm with base e (approximately 2.718), denoted as ln(x).

Front

Evaluate log₂8.

Back

log₂8 = 3, because 2³ = 8.

Front

If log_pt = m, what is t in terms of p and m?

Back

t = p^m.

Front

Rewrite the equation 5³ = 125 in logarithmic form.

Back

log₅125 = 3.