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Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

4. Solving Exponential Equations

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Exercise 20 Page 303

When we rewrite fractions as an exponential term, do we use positive or negative exponents?

Error: 18 ≠ 2^3
Solution: x=- 2

Practice makes perfect

Finding the Error

Let's start by finding where the error occurred. we will begin with the first step. (1/8)^(5x)&=32^(x+8) * &⇓ (2^3)^(5x)&=(2^5)^(x+8)

The error occurred when rewriting ( 18)^(5x) as (2^3)^(5x). The real value of 2^3 is 8, not 18.

Correctly Solving the Equation

We will now correctly solve this equation. Knowing that 2^3=8, we can rewrite 18 as 12^3.

(1/8)^(5x)=32^(x+8)

Rewrite 1/8 as 1/2^3

(1/2^3)^(5x)=32^(x+8)

FracToNegExponent

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

(2^(- 3))^(5x)=32^(x+8)

Rewrite 32 as 2^5

(2^(- 3))^(5x)=(2^5)^(x+8)

FracToNegExponent

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

(2^(- 3))^(5x)=(2^5)^(x+8)

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

2^(- 15x)=2^(5x+40)

EquateExponents

Equate exponents

- 15x=5x+40

▼

Solve for x

LHS-5x=RHS-5x

- 20x=40

.LHS /(- 20).=.RHS /(- 20).

x=- 2

When solved correctly, x=- 2.

Subchapter links

Communicate Your Answer p.299

Monitoring Progress p.300-302

Exercises p.303-304