7.6 Properties of Logs

Front

What is the property of logarithms that states \( \log\left(\frac{m}{n}\right) \) can be expressed as?

Back

\( \log m - \log n \) (Quotient Rule)

Front

What is the property of logarithms that states \( \log(m^n) \) can be expressed as?

Back

\( n \log m \) (Power Rule)

Front

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

Back

\( 6^2 = 36 \)

Front

What is the property of logarithms that states \( \log(xy) \) can be expressed as?

Back

\( \log x + \log y \) (Product Rule)

Front

Express \( \log_b \left( \frac{x}{y} \right) \) as two logs.

Back

\( \log_b x - \log_b y \)

Front

What is the value of \( \log_{10} 1000 \)?

Back

3 (since \( 10^3 = 1000 \))

Front

If \( \log_a b = c \), what is the equivalent exponential form?

Back

\( a^c = b \)

Front

What is the change of base formula for logarithms?

Back

\( \log_b a = \frac{\log_k a}{\log_k b} \) for any base \( k \) (usually 10 or e)

Front

What is the value of \( \log_2 8 \)?

Back

3 (since \( 2^3 = 8 \))

Front

What is the logarithmic identity for \( \log_b 1 \)?

Back

0 (since \( b^0 = 1 \))