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Big Ideas Math Integrated I, 2016 View details

4. Solving Exponential Equations

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Exercise 38 Page 304

Rewrite the terms so that they have a common base.

x=8

Practice makes perfect

To solve the given exponential equation, we will start by rewriting the terms so that they have a common base.

12 * 2^(x-7) = 24

DivEqn

.LHS /12.=.RHS /12.

2^(x-7) = 24/12

CalcQuot

Calculate quotient

2^(x-7) = 2

a=a^1

2^(x-7) = 2^1

Now, we have two equivalent expressions with the same base. The Property of Equality for Exponential Equations says that if both sides of the equation are equal, the exponents must also be equal. 2^(x-7) = 2^1 ⇔ x-7 = 1 Finally, we will solve the equation x-7 = 1 by adding 7 to both sides of the equation. \begin{gathered} x-7

= 1 \quad \Leftrightarrow \quad x = 8 \end{gathered}