WECHS 10 th Grade Math December 16, 2010 Test December 17

 Logarithms ◦ Convert between log and exponential form ◦ Evaluate logs – get numerical answer ◦ Expand logs using log properties ◦ Simplify logs using log properties ◦ Solve exponential equation using log  Rational exponents ◦ Convert between radical and exponential form ◦ Evaluate – get numerical answer  Exponential review – calculate growth or decay

Swap between forms: LOGEXPONENTIAL

Product Property  Log b (x·y) = Log b x + Log b y Quotient Property  Log b (x ÷ y) = Log b x - Log b y Power Property  Log b x y = y·Log b x Log of Base  Log b b = 1 Log of 1  Log b 1=0

When you have the question “log b a = x” (b and a will be numbers), ask “b to what power equals a?” Ex:  Log 3 27 = ?3 to what power equals 27?  Log 5 25 = ?5 to what power equals 25?  Log.01 = ?10 to what power equals.01? If you have a fractional base, flip the fraction over and make the answer negative. Log ⅓ 9 = ? Log 3 9 = -x -x = 2x = -2

 Each factor should be split off into its own log, using the Product or Quotient Property. ◦ Log 6 (2xy) = Log Log 6 x + Log 6 y  Split into separate logs before using the Power Property to remove exponents. ◦ Log 5 4x 2 = Log Log 5 x 2 = Log Log 5 x  Except – if a power applies to more than one factor, do that first. ◦ Log(2x) 3 = 3Log2x = 3(Log2 + Logx)

 The opposite of expanding – combine everything into a single log if possible. ◦ Logx + Logy + Log6 = Log6xy  Move factors outside the log up to be exponents before combining terms. ◦ 3Logx + 2logy = Logx 3 + Logy 2 = Logx 3 y 2

 If you have an equation with variable in the exponent, take log of both sides.  Ex: solve 3 x = 18

 A rational exponent is a fraction in the exponent: ◦ Ex: x ⅓, y ⅗, z ⅝  This can be written in radical or exponent form:

 Write in radical form:  Write in exponent form:

 Take root first if possible so you work with smaller numbers; then raise to a power.  You can raise to a power first if it is not possible to take the root.

 x m ·x n = x (m+n) .  (x m ) n = x mn .

 Exponential functions show things that grow or decay/depreciate at a constant rate:  A is the initial amount (principle).  r is the growth rate (as a decimal)  If it is a growth problem, r is positive and the number in ( ) is greater than 1  If it is a decay problem, r is negative, and the number in ( ) is less than 1.