College Algebra & Trigonometry, 2018a

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3.3. SOLVING EXPONENTIAL EQUATIONS 167 Since the log base 10 and log base e are both programmed into most calculators, these are the most commonly used bases for logarithms. Example Solve for x. 5 2x+3 =17 We start this problem in the same fashion, but this time we will use a logarithm to the base e: 5 2x+3 =17 ln 5 2x+3 =ln17 (2x +3)ln5=ln17 There are several possibilities for finishing the problem from this point. We will focus on two of them that are the most useful for solving more complex problems. First, we will distribute the ln 5 into the parentheses and then get the x by itself. (2x +3)ln5=ln17 x ∗ 2 ln 5 + 3 ln 5 = ln 17 −3ln5=−3ln5 x ∗ 2ln5=ln17− 3ln5 x = ln 17 − 3ln5 2ln5 ≈−0.620 And we can check the answer by plugging it back in: 5 2∗(−0.0620)+3 ≈ 5 1.760 ≈ 16.9897 ≈ 17
168 CHAPTER 3. EXPONENTS AND LOGARITHMS We can also approximate the logarithms in the problem and solve for an approximate answer: (2x +3)ln5=ln17 x ∗ 2 ln 5 + 3 ln 5 = ln 17 3.2189x +4.8283 ≈ 2.8332 −4.8283 ≈−4.8283 3.2189x ≈−1.9951 x ≈−0.620 If you use the method of approximating, it’s important to make a good approximation. At least 4-5 decimal places are necessary for an accurate answer. Let’s look at an example that has variables on both sides of the equation: Example Solve for x. 4 3x =9 2x−1 We’ll use log base 10 in this problem. 4 3x =9 2x−1 log 4 3x =log9 2x−1 3x ∗ log4=(2x − 1) log 9 x ∗ 3log4=x ∗ 2log9− log 9
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College Algebra & Trigonometry
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c○2018 Richard W. Beveridge This
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4 CONTENTS 2.4 Solution of Rational
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6 CONTENTS 8.2 The Trigonometric Ra
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8 CONTENTS
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88 CHAPTER 2. POLYNOMIAL AND RATION
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100 CHAPTER 2. POLYNOMIAL AND RATIO
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288 CHAPTER 6. SEQUENCES AND SERIES
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472 CHAPTER 11. THE LAW OF SINES TH
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College Algebra & Trigonometry, 2018a

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