Front

What is the value of \( \log_{\frac{1}{2}} \frac{1}{32} \)?

Back

5

Front

Is the function \( f(x) = \log_5(x + 4) - 2 \) increasing or decreasing?

Back

increasing

Front

Expand the logarithmic expression \( \log \frac{k^3}{2} \).

Back

\( 3 \log k - \log 2 \)

Front

Solve for \( x \) in the equation \( \log_8(x) = 2 \).

Back

\( x = 64 \)

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 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 product rule for logarithms?

Back

\( \log_b(mn) = \log_b(m) + \log_b(n) \) for any positive numbers \( m \) and \( n \).

Front

What is the quotient rule for logarithms?

Back

\( \log_b\left(\frac{m}{n}\right) = \log_b(m) - \log_b(n) \) for any positive numbers \( m \) and \( n \).

Front

What is the power rule for logarithms?

Back

\( \log_b(m^p) = p \log_b(m) \) for any positive number \( m \) and any real number \( p \).

Front

What is the value of \( \log_5(25) \)?

Back

2