489 4.5 Exponential and Logarithmic Equations Use properties of logarithms to rewrite each function, and describe how the graph of the given function compares to the graph of g1x2 = ln x. 103. ƒ1x2 = ln 1e2x2 104. ƒ1x2 = ln x e 105. ƒ1x2 = ln x e2 1. For the one-to-one function ƒ1x2 = 23 3x - 6, find ƒ-11x2. 2. Solve 42x+1 = 83x-6. 3. Graph ƒ1x2 = -3x. Give the domain and range. 4. Graph ƒ1x2 = log4 1x + 22. Give the domain and range. 5. Future Value Suppose that $15,000 is deposited in a bank certificate of deposit at an annual rate of 2.7% for 8 yr. Find the future value if interest is compounded as follows. (a) annually (b) quarterly (c) monthly (d) daily (365 days) 6. Use a calculator to evaluate each logarithm to four decimal places. (a) log 34.56 (b) ln 34.56 7. What is the meaning of the expression log6 25? 8. Solve each equation. (a) x = 3log3 4 (b) log x 25 = 2 (c) log4 x = -2 9. Assuming all variables represent positive real numbers, use properties of logarithms to rewrite log3 2x # y pq4 . 10. Given logb 9 = 3.1699 and logb 5 = 2.3219, find the value of logb 225. 11. Find the value of log3 40 to four decimal places. 12. If ƒ1x2 = 4x, what is the value of ƒ1log 4 122? Chapter 4 Quiz (Sections 4.1– 4.4) Exponential Equations We solved exponential equations in earlier sections. General methods for solving these equations depend on the property below, which follows from the fact that logarithmic functions are one-to-one. 4.5 Exponential and Logarithmic Equations ■ Exponential Equations ■ Logarithmic Equations ■ Applications and Models Property of Logarithms If x 70, y 70, a 70, and a≠1, then the following holds true. x =y is equivalent to loga x =loga y.
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