Exercise 7 Page 301

Rewrite the terms so that they have a common base.

x = -2

Practice makes perfect

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

(1/3)^(x-1) = 27

1/a=a^(- 1)

(3^(-1))^(x-1) = 27

WritePow

Write as a power

(3^(-1))^(x-1) = 3^3

PowPow

(a^m)^n=a^(m* n)

3^(-1(x-1)) = 3^3

Distr

Distribute -1

3^(- x+1) = 3^3

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^{\text{-} x+1} = 3^3 \quad \Leftrightarrow \quad \text{-} x+1 = 3 \end{gathered} Finally, we will solve the equation - x+1 = 3.

- x+1 = 3

SubEqn

LHS-1=RHS-1

- x = 2

DivEqn

.LHS /(-1).=.RHS /(-1).

x=2/-1

MoveNegDenomToFrac

Put minus sign in front of fraction

x = -2/1

DivByOne

a/1=a

x = -2

To check our answer, we will substitute -2 for x in the given equation.

(1/3)^(x-1) = 27

Substitute

x= -2

(1/3)^(-2-1) ? = 27

SubTerm

Subtract term

(1/3)^(-3) ? = 27

1/a=a^(- 1)

(3^(-1))^(-3) ? = 27

PowPow

(a^m)^n=a^(m* n)

3^(-1(-3)) ? = 27

MultNegNegOnePar

- a(- b)=a* b

3^3 ? = 27

CalcPow

Calculate power

27 = 27 ✓

Since substituting -2 for x in the given equation produces a true statement, x=-2 is the solution to our equation.

Subchapter links

Communicate Your Answer p.299

Monitoring Progress p.300-302

Exercises p.303-304

Exercise 7 Page 301

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