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

Convert the exponential equation 2^3 = 8 into logarithmic form.

Back

log_2(8) = 3.

Front

What is the base of a logarithm?

Back

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

Front

Write the logarithmic expression log_5(25) in exponential form.

Back

5^2 = 25.

Front

If log_2(x) = 4, what is the value of x?

Back

x = 2^4 = 16.

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

Convert log_3(81) = 4 into exponential form.

Back

3^4 = 81.

Front

What is the value of log_10(1000)?

Back

log_10(1000) = 3, because 10^3 = 1000.

Front

Write log_2(1/8) in exponential form.

Back

2^(-3) = 1/8.

Front

If log_4(16) = x, what is the value of x?

Back

x = 2, because 4^2 = 16.