Review: Exponents and Logarithms

Front

What is the definition of an exponent?

Back

An exponent is a number that indicates how many times to multiply the base by itself. For example, in 2^3, 2 is the base and 3 is the exponent, meaning 2 is multiplied by itself 3 times (2 * 2 * 2 = 8).

Front

What is the definition of a logarithm?

Back

A logarithm is the inverse operation to exponentiation, indicating the power to which a base must be raised to produce a given number. For example, log_2(8) = 3 because 2^3 = 8.

Front

Evaluate: 3 log_2(4)

Back

6

Front

Rewrite the exponential equation x^6 = 64 into its logarithmic form.

Back

log_x(64) = 6

Front

Write in logarithmic form: 2^-4 = 1/16

Back

log_2(1/16) = -4

Front

Rewrite log_p(t) = m in exponential form.

Back

p^m = t

Front

Write in exponential form: log_2(32) = 5

Back

2^5 = 32

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 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).