Practice with logs

Front

What is the product property of logarithms?

Back

The product property states that log_b(mn) = log_b(m) + log_b(n), meaning the log of a product is the sum of the logs.

Front

What is the quotient property of logarithms?

Back

The quotient property states that log_b(m/n) = log_b(m) - log_b(n), meaning the log of a quotient is the difference of the logs.

Front

What is the power property of logarithms?

Back

The power property states that log_b(m^k) = k * log_b(m), meaning the log of a number raised to a power is the power times the log of the number.

Front

How do you combine logarithmic expressions that are added together?

Back

When combining logarithmic expressions that are added, you multiply the arguments: log_b(m) + log_b(n) = log_b(mn).

Front

How do you combine logarithmic expressions that are subtracted?

Back

When combining logarithmic expressions that are subtracted, you divide the arguments: log_b(m) - log_b(n) = log_b(m/n).

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, allowing you to convert logs to a different base.

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: if b^y = x, then log_b(x) = y.

Front

What is the value of log_b(b)?

Back

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

Front

What is the value of log_b(1)?

Back

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

Front

How do you express log(12) + 2log(x) as a single logarithm?

Back

You can express it as log(12x^2) using the product and power properties of logarithms.