Evaluating 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 log_b(b) equal to?

Back

log_b(b) = 1, because any number raised to the power of 1 is itself.

Front

What is log_b(1) equal to?

Back

log_b(1) = 0, because any number raised to the power of 0 is 1.

Front

How do you evaluate log_3(9)?

Back

log_3(9) = 2, because 3^2 = 9.

Front

How do you evaluate log_25(5)?

Back

log_25(5) = 1/2, because 25^(1/2) = 5.

Front

What is the value of log(1/10,000)?

Back

log(1/10,000) = -4, because 10^(-4) = 1/10,000.

Front

What is the relationship between logarithms and exponents?

Back

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

Front

How do you evaluate log_2(16)?

Back

log_2(16) = 4, because 2^4 = 16.

Front

What is the product rule for logarithms?

Back

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