Properties of Logs Practice

Front

What is the property of logarithms that allows you to condense \( \log a - \log b \)?

Back

\( \log a - \log b = \log \left( \frac{a}{b} \right) \)

Front

Convert \( \log_2 32 = 5 \) into exponential form.

Back

\( 2^5 = 32 \)

Front

What is the result of condensing \( 3 \log 11 \)?

Back

\( \log 11^3 = \log 1331 \)

Front

Rewrite \( 3^4 = 81 \) in logarithmic form.

Back

\( \log_3 81 = 4 \)

Front

Convert \( 5^2 = 25 \) into logarithmic form.

Back

\( \log_5 25 = 2 \)

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 logarithmic identity for \( \log a + \log b \)?

Back

\( \log a + \log b = \log (a \cdot b) \)

Front

If \( \log_b x = y \), what is the equivalent exponential form?

Back

\( b^y = x \)

Front

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

Back

3, because \( 10^3 = 1000 \)

Front

What is the logarithmic property for \( \log a^n \)?

Back

\( \log a^n = n \cdot \log a \)