Exercise 19 Page 323

Rewrite the terms so that they have a common base.

x=- 4

Practice makes perfect

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

(1/16)^(3x)=64^(2(x+8))

WritePow

Write as a power

(1/2^4)^(3x)=(2^6)^(2(x+8))

1/a=a^(- 1)

(2^(- 4))^(3x)=(2^6)^(2(x+8))

PowPow

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

2^(- 12x)=2^(12(x+8))

Now, we have two equivalent expressions with the same base. If both sides of the equation are equal, the exponents must also be equal. 2^(- 12x)=2^(12(x+8)) ⇔ - 12x=12(x+8) Finally, we will solve the equation - 12x=12(x+8).

- 12x=12(x+8)

Distr

Distribute 12

- 12x=12x+96

SubEqn

LHS-12x=RHS-12x

- 24x=96

DivEqn

.LHS /- 24.=.RHS /- 24.

x=- 4

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 19 Page 323

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