Exercise 5 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.

9^(2x) = 3^(x-6)

WritePow

Write as a power

(3^2)^(2x) = 3^(x-6)

PowPow

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

3^(2*2x) = 3^(x-6)

Multiply

3^(4x) = 3^(x-6)

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} = 3^{x-6} \quad \Leftrightarrow \quad 4x = x-6 \end{gathered} Finally, we will solve the equation 4x = x-6.

4x = x-6

SubEqn

LHS-x=RHS-x

3x = -6

DivEqn

.LHS /3.=.RHS /3.

x=-6/3

MoveNegNumToFrac

Put minus sign in front of fraction

x=-6/3

CalcQuot

Calculate quotient

x=-2

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

9^(2x) = 3^(x-6)

Substitute

x= -2

9^(2( -2)) ? = 3^(-2-6)

MultPosNeg

a(- b)=- a * b

9^(-4) ? = 3^(-2-6)

SubTerm

Subtract term

9^(-4) ? = 3^(-8)

WritePow

Write as a power

( 3^2 )^(-4) ? = 3^(-8)

PowPow

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

3^(2*(-4)) ? = 3^(-8)

MultPosNeg

a(- b)=- a * b

3^(-8) = 3^(-8) ✓

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 5 Page 301

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