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McGraw Hill Integrated II, 2012

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McGraw Hill Integrated II, 2012 View details

Study Guide and Review

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Exercise 15 Page 265

Rewrite the terms so that they have a common base.

y=9/41

Practice makes perfect

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

8^(3-3y) = 256^(4y)

Write as a power

8^(3-3y) = ( 16^2)^(4y)

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

8^(3-3y) = 16^(2 * 4y)

Multiply

8^(3-3y) = 16^(8y)

Write as a power

(2^3)^(3-3y) = ( 2^4)^(8y)

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

2^(3(3-3y)) = 2^(4 * 8y)

Distribute 3

2^(9-9y) = 2^(4 * 8y)

Multiply

2^(9-9y) = 2^(32y)

Now we have two equivalent expressions with the same base. If both sides of the equation are equal, the exponents must also be equal. 2^(9-9y) = 2^(32y) ⇔ 9-9y = 32y Finally, we will solve the equation 9-9y = 32y.

9-9y = 32y

LHS+9y=RHS+9y

9 = 41y

.LHS /41.=.RHS /41.

9/41=y

Rearrange equation

y = 9/41

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