Basic 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, 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

Convert the exponential equation 5^x = 17 to logarithmic form.

Back

x = log_5(17).

Front

What is log_5(25)?

Back

log_5(25) = 2 because 5^2 = 25.

Front

What is the value of log_4(1)?

Back

log_4(1) = 0 because any number raised to the power of 0 equals 1.

Front

What is the value of log_2(16)?

Back

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

Front

If log_5(25) = y, what is the value of y?

Back

y = 2.

Front

Write the logarithmic form of 2^-4 = 1/16.

Back

log_2(1/16) = -4.

Front

What is the value of log_10(1000)?

Back

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

Front

What does DNE stand for in logarithmic terms?

Back

DNE stands for 'Does Not Exist', indicating that the logarithm is undefined.