Chapter6 - Pre-Calculus Chapter 6A Chapter 6A Exponential...

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© : Pre - Calculus - Chapter 6A Chapter 6A - Exponential and Logarithmic Equations Exponential Equations In previous chapters we learned about the exponential and logarithmic functions, studied some of their properties, and learned some of their applications. In this chapter we show how to solve some simple equations which contain the unknown either as an exponent (exponential equation) or as the argument of a logarithmic function. As a general rule of thumb , to solve an exponential equation proceed as follows : 1 . Isolate the expression containing the exponent on one side of the equation. 2 . Take the logarithm of both sides to ”bring down the exponent”. 3 . Solve for the variable. Example 1 : Solve 3 x 25 Solution: 3 x 25 take the natural log of both sides x ln3 ln25 solve for x x ln25 ln3 2. 929947 Example 2 : Solve 4 3 x 1 8 Solution: 4 3 x 1 8 isolate x 3 x 1 4 take the natural log of both sides x 1 ln3 ln4 solve for x x ln4 ln3 1 . 2618595 Example 3 : Solve the equation 10 1 e x 2 Solution We need to “isolate” the terms involving x on one side of the equation. We can do this by cross multilpying and then solving for e x : 1 e x 5 e x 4 x ln4 x ln4 ≈ − 1. 386294 © : Pre - Calculus
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