Logarithmic Functions Practice

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 logarithms and exponents?

Back

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

Front

What is the value of log_10(100)?

Back

2, because 10^2 = 100.

Front

What is the value of log_2(8)?

Back

3, because 2^3 = 8.

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

How do you convert the exponential equation 5^3 = 125 into logarithmic form?

Back

log_5(125) = 3.

Front

How do you convert the logarithmic equation log_4(16) = 2 into exponential form?

Back

4^2 = 16.