(2.9)Simplifying Logarithmic Expressions

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. For example, if \( b^y = x \), then \( \log_b(x) = y \).

Front

Evaluate \( \log_7 343 \).

Back

3

Front

True or False: \( \log_8 64 = 2 \).

Back

True

Front

Rewrite \( \log_2 8 = 3 \) in exponential form.

Back

\( 2^3 = 8 \)

Front

Simplify \( \log_2 \frac{1}{8} \).

Back

-3

Front

Simplify \( \log_7 49 \).

Back

2

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

What is the product rule for logarithms?

Back

The product rule states that \( \log_b(mn) = \log_b(m) + \log_b(n) \).

Front

What is the quotient rule for logarithms?

Back

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

Front

What is the power rule for logarithms?

Back

The power rule states that \( \log_b(m^n) = n \cdot \log_b(m) \).