Math Stuff
- 1. 5.2 – Exponents and Power Functions Product Property- a^m * a^n = a^m+n Quotient Property- a^m/a^n = a^m-n Definiton of Negative- a^-n = 1/a^n Zero Exponents- a^0 = 1 Power of a Power- (a^m)^n = a^m*n Power of a Product- (a*b)^m = a^m*b^m Power Property of Equality- if a = b then a^n = b^n General form of an exponential Function is y = a*b^x General form of a power function is Y = a*x^n
- 2. 5.3 – Rational Exponents and Roots - Properties of exponents only give one solution to an equation because they are only defined for positive bases. - Point-Ratio form is y = y1 * b^x-x1 - x^1/5 is the same as the fifth root of x. EX. 9 th root of b^5 th = 26 B^5/9 = 26 (b^5/9)^9/5 = 26^9/5 B = 352.33
- 3. 5.6 – Logarithmic Functions -log x is another way of expressing x as a power of 10, which is the commonly used base for logarithms. -a logarithm is: for a > 0 and b > 0, (logb)a = x is equivalent to a = b^x -Log change of base = (logb)a = loga/logb EX: 4^x = 128 4^3 = 64 and 4^4 = 256, so must be between 3 and 4 (10log4)^x = (10log128) 10^x log 4 = 10log128 X log 4 = log 128 X = log 128/log 4 = 3.5
- 4. 5.7- Properties of Logarithms -Definition of Logarithm: if x = a^m, then (loga)x = m -Product Property: a^m * a^n = a^m+n -Quotient Property: a^m/a^n = a^m-n -Power Property: (loga)x^n = n (loga)x -Power of a Power Property: (a^m)^n = a^m*n -Power of a Quotient Property: (a/b)^n = a^n/b^n -Change of Base: (loga)x = (logb)x/(logb)a -Def. Of Rational Exponents: a^m/n = n root of a ^ m -Def. Of Negative Exponents: a^-n = 1/a^n