1 Review - Logarithms

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

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

Convert the logarithmic equation log_6(36) = 2 to exponential form.

Back

6^2 = 36.

Front

What is the value of log_3(81)?

Back

4, because 3^4 = 81.

Front

If log_b(x) = y, what is the equivalent exponential form?

Back

b^y = x.

Front

Solve for x: 3^x = 27.

Back

x = 3, because 27 = 3^3.

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^p) = p * log_b(m).

Front

Evaluate: log_10(1000).

Back

3, because 10^3 = 1000.