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Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

4. Solving Exponential Equations

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Exercise 39 Page 304

Rewrite the terms so that they have a common base.

x=-3

Practice makes perfect

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

4 (3^(-2x-4)) = 36

.LHS /4.=.RHS /4.

3^(-2x-4) = 36/4

Calculate quotient

3^(-2x-4) = 9

Write as a power

3^(-2x-4) = 3^2

Now, we have two equivalent expressions with the same base. The Property of Equality for Exponential Functions says that if both sides of the equation are equal, the exponents must also be equal. 3^(-2x-4) = 3^2 ⇔ -2x-4 = 2 Finally, we will solve the equation -2x-4 = 2.

-2x-4 = 2

LHS+4=RHS+4

-2x = 6

.LHS /(-2).=.RHS /(-2).

x = 6/-2

MoveNegDenomToFrac

Put minus sign in front of fraction

x = -6/2

Calculate quotient

x = -3

Subchapter links

Communicate Your Answer p.299

Monitoring Progress p.300-302

Exercises p.303-304