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.

McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

Study Guide and Review

Continue to next subchapter

Exercise 13 Page 265

Rewrite the terms so that they have a common base.

x=-7

Practice makes perfect

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

3^(4x) = 9^(3x+7)

Write as a power

3^(4x) = ( 3^2 )^(3x+7)

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

3^(4x) = 3^(2 * (3x+7))

Distribute 2

3^(4x) = 3^(6x+14)

Now, we have two equivalent expressions with the same base. If both sides of the equation are equal, the exponents must also be equal. 3^(4x) = 3^(6x+14) ⇔ 4x = 6x+14 Finally, we will solve the equation 4x = 6x+14.

4x = 6x+14

LHS-6x=RHS-6x

-2x = 14

.LHS /(-2).=.RHS /(-2).

x=-7

Subchapter links

1 Graphing Exponential Functions p.265

2 Solving Exponential Equations and Inequalities p.265

3 Simplifying Radical Expressions p.265

4 Operations with Radical Expressions p.266

5 Radical Equations p.266