Exponential and Log Functions Review

Front

Rewrite the logarithm in exponential form: \(\log_2 x = 10\)

Back

\(2^{10} = x\)

Front

Solve \(2^x = 16\)

Back

\(x = 4\)

Front

Condense: \(\log_3 x + \log_3 y = ?\)

Back

\(\log_3 (x \cdot y)\)

Front

Evaluate: \(\log_5 \left(\frac{1}{25}\right) = ?\)

Back

\(-2\)

Front

Solve \(10^x = 100^{(x-1)}\)

Back

\(x = 2\)

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

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 product rule for logarithms?

Back

\(\log_b (xy) = \log_b x + \log_b y\) for any positive numbers \(x\) and \(y\).

Front

What is the quotient rule for logarithms?

Back

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

Front

What is the power rule for logarithms?

Back

\(\log_b (x^k) = k \cdot \log_b x\) for any positive number \(x\) and real number \(k\).