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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

2. Solving Exponential Equations and Inequalities

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Exercise 1 Page 240

Rewrite the terms so that they have a common base.

x=12

Practice makes perfect

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

3^(5x)=27^(2x-4)

Write as a power

3^(5x)=( 3^3 )^(2x-4)

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

3^(5x)=3^(3(2x-4))

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^(5x)=3^(3(2x-4)) ⇔ 5x= 3(2x-4) Finally, we will solve the equation 5x=3(2x-4).

5x=3(2x-4)

▼

Solve for x

Distribute 3

5x=6x-12

LHS-6x=RHS-6x

- x=- 12

LHS * (-1)=RHS* (-1)

x=12

Subchapter links

Exercises p.240-243