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Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

Chapter Test

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Exercise 8 Page 325

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.

256^(x+2)=16^(3x-1)

Write as a power

( 16^2 )^(x+2)=16^(3x-1)

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

16^(2x+4)=16^(3x-1)

Now, we have two equivalent expressions with the same base. If both sides of the equation are equal, the exponents must also be equal. 16^(2x+4)=16^(3x-1) ⇔ 2x+4=3x-1 Finally, we will solve the equation 2x+4=3x-1.

2x+4=3x-1

LHS-3x=RHS-3x

- x +4 =- 1

LHS-4=RHS-4

- x = - 5

LHS * (- 1)=RHS* (- 1)

x=5

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Exercises p.325