Logarithms and Exponents

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

What is the relationship between exponents and logarithms?

Back

Exponents and logarithms are inverse operations. If b^y = x, then log_b(x) = y.

Front

What is the value of log_10(100)?

Back

log_10(100) = 2, because 10^2 = 100.

Front

What is the product rule for logarithms?

Back

The product rule states that log_b(xy) = log_b(x) + log_b(y).

Front

What is the quotient rule for logarithms?

Back

The quotient rule states that log_b(x/y) = log_b(x) - log_b(y).

Front

What is the power rule for logarithms?

Back

The power rule states that log_b(x^k) = k * log_b(x).

Front

Solve for x: log_2(8) = x

Back

x = 3, because 2^3 = 8.

Front

Evaluate: log_4(16)

Back

log_4(16) = 2, because 4^2 = 16.

Front

What is the value of log_e(e^3)?

Back

log_e(e^3) = 3, because e^3 = e^3.