By: James Morgan, Rachel Martin, and Mitch Essinger Chapter 5 Review By: James Morgan, Rachel Martin, and Mitch Essinger

Chapter 5 Working with Positive Square Roots The square root of a number is the value that, when squared, gives back the original number. Perfect squares are integers that have integer square roots.

5.2 Properties of Exponents and Power Functions To simplify an expression or an equation, you need to rewrite it in exponential function. For a> 0, b> 0, and all values of m and n, the following properties apply; Product Property of Exponents, Quotient Property of Exponents, Definition of Negative Exponents, Zero Exponents, Power of a Power Property, Power of a Product Property, Power Property of Equality, Common Base Property of Equality, and Power of a Quotient Property. To solve a power equation, use the power of a power property and choose an exponent that will undo the exponent on x.

5.3 Rational Exponents and Roots Rational exponents with numerator 1 indicate positive roots. For rational exponents with numerators other than 1, the numerator is interpreted as the exponent to which to raise the root. The equation for an exponential curve can be written using point-ratio form if you know a point on the curve and the common ratio between points that are 1 horizontal unit apart.

5.6 Logarithmic Functions The expression log x is another way of expressing x as a power of 10, called a common logarithm. The general logarithmic function is an exponent-producing function. When bases other than 10 are used, you must specify the base by using a subscript.

5.7 Properties of Logarithms During the seventeenth century, the Scottish mathematician John Napier, discovered a quick easy method using a number table he names the logarithms Because logarithms are exponents, they must have properties similar to the properties of exponents.