LP 6 Test: Logarithms

Front

Write as an exponential expression: \( \log(100) = x \)

Back

\( 10^x = 100 \)

Front

What is the base of the natural logarithm?

Back

e

Front

Combine into one logarithm and evaluate: \( \log_5\left(\frac{1}{8}\right) + \log_5(8) \)

Back

0

Front

Evaluate \( \log_3\left(\frac{1}{81}\right) \)

Back

-4

Front

Evaluate \( \log_{36}(6) \)

Back

\( \frac{1}{2} \)

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

If \( \log_b(a) = c \), what is the equivalent exponential form?

Back

\( b^c = a \)

Front

What is the change of base formula for logarithms?

Back

\( \log_b(a) = \frac{\log_k(a)}{\log_k(b)} \) for any base \( k \) > 0.

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.