Log Properties Mixed Practice

Front

What is the property of logarithms that allows you to combine two logs with the same base by addition?

Back

The property states that \( \log_b(m) + \log_b(n) = \log_b(m \cdot n) \).

Front

What is the property of logarithms that allows you to combine two logs with the same base by subtraction?

Back

The property states that \( \log_b(m) - \log_b(n) = \log_b\left(\frac{m}{n}\right) \).

Front

What is the change of base formula for logarithms?

Back

The change of base formula states that \( \log_b(a) = \frac{\log_k(a)}{\log_k(b)} \) for any positive base \( k \).

Front

How do you express \( \log_3(t) = 5 \) in exponential form?

Back

In exponential form, it is expressed as \( 3^5 = t \).

Front

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

Back

The identity states that \( \log_b(b) = 1 \).

Front

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

Back

The identity states that \( \log_b(1) = 0 \).

Front

How do you simplify \( \ln\left(\frac{a}{b}\right) \)?

Back

It simplifies to \( \ln(a) - \ln(b) \).

Front

What is the result of \( \log_b(m^n) \)?

Back

The result is \( n \cdot \log_b(m) \).

Front

How do you express \( \log(12x^2) - \log(6x) \) as a single logarithm?

Back

It simplifies to \( \log(2x) \).

Front

What is the result of \( \log_3(2) + \log_3(5x) - \log_3(7) \)?

Back

It simplifies to \( \log_3\left(\frac{10x}{7}\right) \).