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a) Use a calculator to approximate each to the nearest thousandth. b) Explain what a logarithm is, you can refer to part a if you would like to. 19) log 7 50 20) log 2 8 Expand each logarithm. 21) log 5 (x5y2) 22) log 3 3 u × v × w Condense each expression to a single logarithm. 23) 2log 2 x - 4log 2 y24) 3log 9 u + 5log 9 v Solve each equation.
Express the equation in exponential form and solve the resulting exponential equation. Simplify the expressions in the equation by using the laws of logarithms. Represent the sums or differences of logs as single logarithms. Square all logarithmic expressions and solve the resulting quadratic equation. ____ 13.
1 EXPONENTS AND LOGARITHMS. WHAT YOU NEED TO KNOW. The rules of exponents: am × an = am+n. am • = am n an. (am)n = amn. m. a n am. a − n = an. an × bn = (ab)n. n an • =⎛ bn ⎝⎜. ⎞. ⎠⎟. The relationship between exponents and logarithms: a = b ⇔ x ga b where a is called the base of the logarithm. loga a x x. a log. x. The rules of logarithms: log. c.
Review 5 Exponents and Logarithms Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Determine the missing value in this table of values for the function y 2x. x y = 2x –1 0.5 0 12 A. 1 C. 0 B. –1 D. 2 ____ 2. Determine the range of y 6x. A. x 0 C. y 0 B. y ò D. y 0
TEST EXPONENTS – LOGARITHMS (without GDC) by Christos Nikolaidis Name:_____ Date:_____ Questions 1. [Maximum mark: 9] Let lnx =a, lny =b and ln5=c. Express the following in terms of a,b and c: (a) 3 25 ln y x (b) log 5 xy (c) log y 5e [3+3+3 marks]
PRACTICE EXAM. 1. All of the following are exponential functions except: y = 1x. y = 2x. y = 3x. 2. The point (-3, n) exists on the exponential graph shown. The value of n is: 3. The graph of. has: A vertical asymptote at x = -3. A horizontal asymptote at x = -3. A vertical asymptote at y = -2. A horizontal asymptote at y = -2. 4.
Test on Exponents and Logarithms (2) (without GDC) by Christos Nikolaidis Date: 28 November 2019 Name of student: _____ 1. [Maximum mark: 6] Let 2 log 3 =a and 2 log 7 b. Express the following in terms of a and b. (a) 2 log 63 [2] (b) 2 log 42 [2] (c) 7 log 3 [2]
