7.6 Properties of Logs

Front

What is the property of logarithms that states \( \log\left(\frac{x}{y}\right) \)?

Back

\( \log x - \log y \) (Quotient Rule)

Front

How can you express \( \log_b\left(\frac{x}{y}\right) \) as two logs?

Back

\( \log_b x - \log_b y \)

Front

Convert the logarithmic equation \( \log_6 36 = 2 \) to exponential form.

Back

\( 6^2 = 36 \)

Front

What is the property of logarithms for \( \log_b(x^n) \)?

Back

\( n \log_b x \) (Power Rule)

Front

How do you combine \( \log_2 x - 5 \log_2 y \) into a single logarithm?

Back

\( \log_2\left(\frac{x}{y^5}\right) \)

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.

Front

What is the change of base formula for logarithms?

Back

\( \log_b a = \frac{\log_k a}{\log_k b} \) for any base \( k \).

Front

What is the product property of logarithms?

Back

\( \log_b(xy) = \log_b x + \log_b y \) (Product Rule)

Front

What is the definition of the base of a logarithm?

Back

The base of a logarithm is the number that is raised to a power to obtain a given value.

Front

How do you express \( \log_b b \)?

Back

\( 1 \) (since any number to the power of 1 is itself).