Logarithms

Front

What is 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 base k.

Front

Evaluate log_3(81).

Back

4

Front

Rewrite the logarithmic equation log_2(1/16) = -4 in exponential form.

Back

2^(-4) = 1/16.

Front

Evaluate 3 log_8(2).

Back

1

Front

What is the base of a logarithm?

Back

The base of a logarithm is the number that is raised to a power to obtain a certain value. In log_b(a), b is the base.

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

Convert the exponential equation 5^3 = 125 to logarithmic form.

Back

log_5(125) = 3.