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Unformatted text preview: x. We summarize
below the two common ways to solve exponential equations, motivated by our examples.
Steps for Solving an Equation involving Exponential Functions
1. Isolate the exponential function.
2. (a) If convenient, express both sides with a common base and equate the exponents.
(b) Otherwise, take the natural log of both sides of the equation and use the Power Rule.
Example 6.3.1. Solve the following equations. Check your answer graphically using a calculator.
1. 23x = 161−x 3. 9 · 3x = 72x 2. 2000 = 1000 · 3−0.1t 4. 75 = 100
1+3e−2t 5. 25x = 5x + 6
6. ex −e−x
2 =5 Solution.
1 You can use natural logs or common logs. We choose natural logs. (In Calculus, you’ll learn these are the most
‘mathy’ of the logarithms.)
This is also the ‘if’ part of the statement logb (u) = logb (w) if and only if u = w in Theorem 6.4.
Please resist the temptation to divide both sides by ‘ln’ instead of ln(2). Just like it wouldn’t make sense to
divide both sides by the square root symbol ‘ ’ when solving x 2 = 5, it makes no sense...
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