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

Logarithms are the inverse operations of exponentiation. If b^c = a, then log_b(a) = c.

Front

Evaluate log_3(81).

Back

4, because 3^4 = 81.

Front

Rewrite the equation 3^4 = 81 in logarithmic form.

Back

log_3(81) = 4.

Front

Evaluate log_3(27).

Back

3, because 3^3 = 27.

Front

Write the equation 5^2 = 25 in logarithmic form.

Back

log_5(25) = 2.

Front

Evaluate log_6(1/216).

Back

-3, because 6^(-3) = 1/216.

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).