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

Write as a power

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

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. \

begin{gathered} 3^{4x-9} = 3^{\text{-}5} \quad \Leftrightarrow \quad 4x-9 = \text{-}5 \end{gathered} Finally, we will solve the equation 4x-9 = -5.

4x-9 = -5

LHS+9=RHS+9

4x = 4

.LHS /4.=.RHS /4.

x = 1

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

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

x= 1

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

a * 1=a

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

Subtract term

3^(-5) ? = 1/243

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

1/3^5 ? = 1/243

Calculate power

1/243 = 1/243 ✓

Since substituting 1 for x in the given equation produces a true statement, x=1 is the solution to our equation.

Communicate Your Answer p.299

Monitoring Progress p.300-302

Exercises p.303-304

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