Exercise 14 Page 265

Rewrite the terms so that they have a common base.

n=- 3/4

Practice makes perfect

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

64^(3n) = 8^(2n-3)

WritePow

Write as a power

(8^2)^(3n) = 8^(2n-3)

PowPow

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

8^(2 * 3n) = 8^(2n-3)

Multiply

8^(6n) = 8^(2n-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. 8^(6n) = 8^(2n-3) ⇔ 6n = 2n-3 Finally, we will solve the equation 6n = 2n-3.

6n = 2n-3

SubEqn

LHS-2n=RHS-2n

4n = -3

DivEqn

.LHS /4.=.RHS /4.

n=-3/4

MoveNegNumToFrac

Put minus sign in front of fraction

n = - 3/4

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 14 Page 265

Hints

Check the answer

Practice exercises

Asses your skill