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)

WritePow

Write as a power

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

PowPow

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

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

Distr

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

SubEqn

LHS-6x=RHS-6x

-2x = 14

DivEqn

.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

Exercise 13 Page 265

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