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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 3 Page 300

If both sides of the equation are equal, the exponents must also be equal.

x=-2

Practice makes perfect

To solve the given exponential equation, note that we have two equivalent expressions with the same base. If both sides of the equation are equal, the exponents must also be equal. 7^(3x+5) = 7^(x+1) ⇔ 3x+5 = x+1Finally, we will solve the equation 3x+5 = x+1.

3x+5 = x+1

LHS-x=RHS-x

2x+5 = 1

LHS-5=RHS-5

2x = -4

.LHS /2.=.RHS /2.

x=-4/2

MoveNegNumToFrac

Put minus sign in front of fraction

x=-4/2

Calculate quotient

x = -2

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

7^(3x+5) = 7^(x+1)

x= -2

7^(3( -2)+5) ? = 7^(-2+1)

a(- b)=- a * b

7^(-6+5) ? = 7^(-2+1)

Add terms

7^(-1) = 7^(-1) ✓

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