Logarithm Basics

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

Rewrite the exponential equation 2^3 = 8 in logarithmic form.

Back

log_2(8) = 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 k.

Front

What is the value of log_10(100)?

Back

2, because 10^2 = 100.

Front

Rewrite log_3(81) = 4 in exponential form.

Back

3^4 = 81.

Front

What is the product rule for logarithms?

Back

The product rule states that log_b(m * n) = log_b(m) + log_b(n).

Front

What is the quotient rule for logarithms?

Back

The quotient rule states that log_b(m / n) = log_b(m) - log_b(n).

Front

What is the power rule for logarithms?

Back

The power rule states that log_b(m^n) = n * log_b(m).

Front

Rewrite log_5(25) in exponential form.

Back

5^2 = 25.

Front

What is the value of log_2(8)?

Back

3, because 2^3 = 8.