Exercise 20 Page 323

Rewrite the terms so that they have a common base.

x=5

Practice makes perfect

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

27^(2x+2)=81^(x+4)

WritePow

Write as a power

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

PowPow

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

3^(6x+6)=3^(4x+16)

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^(6x+6)=3^(4x+16) ⇔ 6x+6=4x+16 Finally, we will solve the equation 6x+6=4x+16.

6x+6=4x+16

SubEqn

LHS-6=RHS-6

6x=4x+10

SubEqn

LHS-4x=RHS-4x

2x=10

DivEqn

.LHS /2.=.RHS /2.

x=5

Subchapter links

1 Exponential Functions p.322

2 Exponential Growth and Decay p.322

3 Comparing Linear and Exponential Functions p.323

4 Solving Exponential Equations p.323

5 Geometric Sequences p.324

6 Recursively Defined Sequences p.324

Exercise 20 Page 323

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