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A logarithm is an exponent.

Ch 8 Portfolio Page. Exponential functions are of the form: y = ab x If 0 < b < 1 , the graph represents exponential DECAY. If b > 1 , the graph represents exponential GROWTH. Graph: y = 2 x + 3 (table of values)

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A logarithm is an exponent.

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  1. Ch 8 Portfolio Page Exponential functions are of the form: y = abx If 0 < b < 1, the graph represents exponential DECAY. If b > 1, the graph represents exponential GROWTH. Graph: y = 2x + 3 (table of values) Compound Interest formula: Continuously Compounded Interest formula The Number e e is an irrational number approximately equal to 2.71828 Exponential functions with a base of e are useful for describing continuous growth or decay. A = balance after t years P = principal r = rate n = # times interest is added per year t = time in years A = amount in account, P = principal, r = annual rate of interest, t = time in years A = Pert Ex 2:: Suppose you invest $1,050 at an annual interest rate of 5.5% compounded continuously. How much will you have in the account after five years? Ex 1:How much must you deposit in an account that pays 8% annual interest, compounded monthly, to have a balance of $1,500 after one year? A logarithm is an exponent. Write the equation in exponential form: log464 = 3 ___________________ Write the equation in logarithmic form: 24 = 16 _____________________ logbx = y and by = x are equivalent expressions Evaluate the logarithms: 1) 2) 3) 4) 5) 6) log497 log216 log88 Properties of Logarithms Let a, u, and v be positive numbers such that a ≠ 1, and let n be any real number. Product Property: Quotient Property: Power Property: • Note: There is no property to simplify the logarithm of a sum. log39 log31 log225 M. Murray

  2. USE PROPERTIES OF LOGS TO EXPAND AND CONDENSE Use the properties of logarithms to simplify (condense): (Write as one log expression) 1) 5log3 + 2log2 Use the properties of logarithms to expand: (Write as a sum or difference of logarithms, or use power property) 2) log45 Change of Base formula: Steps to solve Exponential Equations: • ) Isolate power • ) Take log of both sides in same base • logaa = x • Use change of base formula Steps to solve Logarithmic Equations: 1) Use properties of logs, if necessary to condense log expression. 2) Write in exponential form Ex) Solve: 3logx – log 2 = 5 Ex) Solve: 2 + 3x = 4 A natural logarithm (ln) is a log with base e. All the same properties of logs also apply to natural logs. Simplifying Natural Logarithms: 5 ln 2 – ln 4 2) 3 ln x + ln y Solve: 3) ln x = -2 4) ex+1 = 30 Simplify using mental math: 3) ln e 4) ln e35) ln 1 M. Murray

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