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We will learn how to solve basic exponential equations. We will deal with the equations of the form. where a; b > 0 and f ; g are real-valued functions. In our examples these will be simple linear or quadratic functions.
21 Αυγ 2024 · Lecture Notes Exponential Equations page 1 Sample Problems 1.Simplify each of the following expressions. a) 32x+1 9x−1 b) 8b−2 2b+1 r 42b−3 c) 52x−3 ·251−x d) 23x−1 ·32−x 6x+1 2.Solve each of the following equations. a) 5x−2 = 4 b) 5e−3x = 42 c) 22x−3 = 52−x d) 5 ·32x−1 = 22−x e) 3 ·22x−3 = 2 ·5x+2 f) 9x + 4 ...
Sample Exponential and Logarithm Problems 1 Exponential Problems Example 1.1 Solve 1 6 3x 2 = 36x+1. Solution: Note that 1 6 = 6 1 and 36 = 62. Therefore the equation can be written (6 1) 3x 2 = (62)x+1 Using the power of a power property of exponential functions, we can multiply the exponents: 63x+2 = 62x+2 But we know the exponential function ...
There are two strategies used for solving an exponential equation. The first strategy, if possible, is to write each side of the equation using the same base. Both bases, 4 and 32, can be written as powers of base 2. Use the exponent rule for a power to a power (multiply exponents). Since the bases are the same, the exponents must be the same.
Use technology to solve each exponential equation below. Explain your method. e. Can an exponential equation have no solution? more than one solution? f. Can any of the equations in part (d) be solved algebraically by using properties of exponents? Explain your reasoning.
In §5.3.3 and §5.3.4 we looked at the exponential function, and the logarithmic function, and considered their general behaviour. In this chapter we will look in more detail at how to solve exponential and logarithmic equations as well as applications of both the exponential and logarithmic functions. 7.1.1 BASIC RULES OF INDICES
Solve exponential equations with unlike bases. Solve exponential equations by graphing. Exponential equations are equations in which variable expressions occur
