body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

4. Solving Exponential Equations

Continue to next subchapter

Exercise 9 Page 303

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.

7^(x-5) = 49^x

Write as a power

7^(x-5) = ( 7^2 )^x

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

7^(x-5) = 7^(2x)

Now, we have two equivalent expressions with the same base. If both sides of the equation are equal, the exponents must also be equal. 7^(x-5) = 7^(2x) ⇔ x-5=2x Finally, we will solve the equation x-5=2x.

x-5=2x

LHS-2x=RHS-2x

- x-5 = 0

LHS+5=RHS+5

- x = 5

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

x=5/-1

MoveNegDenomToFrac

Put minus sign in front of fraction

x=-5/1

a/1=a

x = -5

To check our answer, we will substitute -5 for x in the given equation.

7^(x-5) = 49^x

x= -5

7^(-5-5) ? = 49^(-5)

Subtract term

7^(-10) ? = 49^(-5)

Write as a power

7^(-10) ? = (7^2)^(-5)

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

7^(-10) ? = 7^(2*(-5))

a(- b)=- a * b

7^(-10) = 7^(-10) ✓

Since substituting -5 for x in the given equation produces a true statement, x=-5 is the solution to our equation.

Subchapter links

Communicate Your Answer p.299

Monitoring Progress p.300-302

Exercises p.303-304