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. For example, in the expression log_b(a) = c, b^c = a.

Front

What is the logarithmic form of the equation 10^3 = 1000?

Back

log_10(1000) = 3.

Front

Evaluate log_2(8).

Back

3, because 2^3 = 8.

Front

What is the change of base formula for logarithms?

Back

log_b(a) = log_k(a) / log_k(b), where k is any positive number.

Front

Evaluate log_10(1).

Back

0, because 10^0 = 1.

Front

What is the value of log_b(b)?

Back

1, because b^1 = b.

Front

Convert log_5(25) = 2 to exponential form.

Back

5^2 = 25.

Front

What is the value of log_3(9)?

Back

2, because 3^2 = 9.

Front

If log_2(x) = 5, what is x?

Back

32, because 2^5 = 32.

Front

What is the product rule for logarithms?

Back

log_b(m * n) = log_b(m) + log_b(n).