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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 13 Page 303

Rewrite the terms so that they have a common base.

x=-3

Practice makes perfect

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

(1/5)^x = 125

1/a=a^(- 1)

(5^(-1))^x = 125

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

5^(-1* x) = 125

Multiply

5^(- x) = 125

Write as a power

5^(- x) = 5^3

Now, we have two equivalent expressions with the same base. If both sides of the equation are equal, the exponents must also be equal. 5^(- x) = 5^3 ⇔ - x = 3 Finally, we will solve the equation - x = 3.

- x = 3

.LHS /(-1).=.RHS /(-1).

x = 3/-1

MoveNegDenomToFrac

Put minus sign in front of fraction

x = -3/1

a/1=a

x = -3

To check our answer, we will substitute -3 for x in the given equation.

(1/5)^x = 125

x= -3

(1/5)^(-3) ? = 125

1/a=a^(- 1)

(5^(-1))^(-3) ? = 125

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

5^(-1(-3)) ? = 125

MultNegNegOnePar

- a(- b)=a* b

5^3 ? = 125

Calculate power

125 = 125 ✓

Since substituting -3 for x in the given equation produces a true statement, x=-3 is the solution to our equation.

Subchapter links

Communicate Your Answer p.299

Monitoring Progress p.300-302

Exercises p.303-304