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Big Ideas Math Integrated I, 2016 View details

4. Solving Exponential Equations

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Exercise 16 Page 303

Rewrite the terms so that they have a common base.

x=1

Practice makes perfect

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

3^(4x-9) = 1/243

WritePow

Write as a power

3^(4x-9) = 1/3^5

FracToNegExponent

1/a^m=a^(- m)

3^(4x-9) = 3^(-5)

Now, we have two equivalent expressions with the same base. If both sides of the equation are equal, the exponents must also be equal. 3^(4x-9) = 3^(-5) ⇔ 4x-9 = -5 Finally, we will solve the equation 4x-9 = -5.

4x-9 = -5

AddEqn

LHS+9=RHS+9

4x = 4

DivEqn

.LHS /4.=.RHS /4.

x = 4/4

QuotOne

a/a=1

x = 1

To check our answer, we will substitute 1 for x in the given equation.

3^(4x-9) = 1/243