7.5 and 7.6 Exponent and Logarithm Rules

Front

Simplify: 7^{-2}

Back

\frac{1}{7^{2}} = \frac{1}{49}

Front

Expand: \log x^{3}y^{7}

Back

3\log x + 7\log y

Front

Simplify: \frac{x^{28}y^{12}}{x^{2}y}

Back

x^{20}y^{8}

Front

Expand: \log \frac{a}{b^{3}}

Back

\log a - 3\log b

Front

Simplify: (c^{5})(c^{3})(c^{3})

Back

c^{11}

Front

Definition: Exponent

Back

An exponent indicates how many times a number (the base) is multiplied by itself.

Front

Definition: Logarithm

Back

The logarithm is the inverse operation to exponentiation, answering the question: to what exponent must a base be raised to produce a given number?

Front

Rule: Product Rule of Logarithms

Back

\log(ab) = \log a + \log b

Front

Rule: Quotient Rule of Logarithms

Back

\log\left(\frac{a}{b}\right) = \log a - \log b

Front

Rule: Power Rule of Logarithms

Back

\log(a^b) = b\log a