hour 3 4. Write the exponential equation 2 = 8 in logarithmic form. a. log38 = 2 c. log23 = 8 b. log28 = 3 d. log82 = 3 ____ ____ 5. Evaluate log4 1 by using mental math. 16 ____ a. 1 c. –2 b. 4 d. 2 4 6. Express log36 + log34.5 as a single logarithm. Simplify‚ if possible. a. 3 c. log310.5 b. log610.5 d. 27 7. Simplify log7x3 − log7x. a. log (x3 − x) 7 ____ c. log72x d. 2(x3 − x) b. 2 log7x ____ x+8 x ____ 8. Solve 8 = 32 . a. x = –12 c. x = 12 b. x = 22 d. x = –22 9. The amount of money
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EXPONENTIAL AND LOGARITHMIC FUNCTIONS I.EXPONENTIAL FUNCTION A. Definition An exponential function is a function defined by f(x) = ax ‚ where a > 0 and a ≠ 1. The domain of the function is the set of real numbers and the range is the set of positive numbers. B. Evaluating Exponential Functions 1. Given: f(x) = 2x‚ find a. f(3) = ____ b. f(5) = _____ c. f(-2) = ______ d. f(-4) = ______ 2. Evaluate f(x) = ( 1)x if 2 a. x = 2 ____ b. x = 4 _____ c. x = -3 ______ d
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Week 2 Complete Lab 1. Solve the exponential equation by expressing each side as a power of the same base and then equating exponents. 6 x = 216 x = 3 2. Solve the exponential equation. Express the solution in terms of natural logarithms. Then use a calculator to obtain a decimal approximation for the solution. ex = 22.8 x= ~3.12676 3. Solve the following logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expression. Give
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Exponential and Logarithmic Functions * Verify that the natural logarithm function defined as an integral has the same properties as the natural logarithm function earlier defined as the inverse of the natural exponential function. Integrals of Exponential and Logarithmic Functions Function | Integral | lnx | x ∙ lnx - x + c | logx | (x ∙ lnx - x) / ln(10) + c | logax | x(logax - logae) + c | ex | ex+c | ek∙x | 1 / k ∙ ek∙x + c | ax | ax / lna + c | xn | 1 / (n+1) ∙ xn+1 +
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Chapter 7 Transcendental Functions Functions can be categorized into two big groups – algebraic and non-algebraic functions. Algebraic functions: Any function constructed from polynomials using algebraic operations (addition‚ subtraction‚ multiplication‚ division and taking roots). All rational functions are algebraic. Transcendental functions are non-algebraic functions. The following are examples of such functions: i. iii. v. Trigonometric functions Exponential functions Hyperbolic functions
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Q1. Prepare a list of objects that you would expect each of the following system to handle a. A program for laying out a newspaper b. A program to compute and store bowling score c. A telephone answering machine d. A controller for DVD writer e. A catalog store order entry system SOLUTION: a. A program for laying out a newspaper: public class Newspaper { Design; News; Pictures: Advertisement; } b. A program to compute and store bowling score. public class bowling { Startbowl;
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MATH 152 MIDTERM I 02.11.2012 P1 P2 P3 Name&Surname: Student ID: TOTAL Instructions. Show all your work. Cell phones are strictly forbidden. Exam Duration : 70 min. 1. Show that 1 p n (ln n) n=2 converges if and only if p > 1: Solution: Apply integral test: Z Z ln R 1 X R 2 1 p dx x (ln x) p=1 p 6= 1 let ln (x) = u then ln 2 so that when p = 1 and p < 1 integral diverges by letting R ! 1‚ so does the series. When p > 1 then integral converges to ! 1 p 1 p 1 p (ln R) (ln 2) (ln
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1. Force of interest 0.05 100 exp Effective rate of return 0.05 100 (1.05) 2 = 102.47 2. The value is 6 6 1 1 × 0.05 2 = 102.53 exp 0.5 δ (s) ds = exp 0.5 (0.01s + 0.04) ds t=6 = exp 0.01 t2 + 0.04t 2 = 1.49. t=0.5 3. 150 in 3 years accumulates to 3 150 exp 0 0.05 + 0.02s2 ds = 150 exp 0.02 t3 + 0.05t 3 t=3 = 208.65 t=0 200 in 5 years accumulates to 3 5 200 exp 0 0.05 + 0.02s2 ds + 3 t=3 0.05 + 0.01s2 ds t3 + 0.05t 3
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Name: Date: Graded Assignment Checkup: Introduction to Logarithms Answer the following questions using what you’ve learned from this lesson. Write your responses in the space provided‚ and turn the assignment in to your instructor. 1. Write the equation y = bx in logarithmic form. logb y 2. Write the equation y = ex in logarithmic form. loge y 3. Write the equation y = log x in exponential form. X = 1y 4. Write the equation y = ln x in exponential form. X = loglny 5. Show two ways
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graphing the basic function and then showing one additional graph for each transformation. Label each graph with at least one point‚ its asymptote‚ and its equation. 5. 6. 7. 8. Using Properties of Logarithms: Express each of the following as a single logarithm and simplify: 9. 10. 11. 12. Solving Exponential Equations - Solve each of the following. 13. 14. 15. 16. Solving Logarithmic Equations - Solve each of the following
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