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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 10: Q. 101 (page 1019)

In the following exercises, solve each equation.
$4^{x + 2} = 64$

Short Answer

Expert verified

The answer is $x = 1$

Step by step solution

01

Step 1. Given

The equation is $4^{x + 2} = 64$

02

Step 2. Solve the equation

$4^{x + 2} = 64 4^{x + 2} = 4^{3}$

Bases are same so the exponents should be equal.

$x + 2 = 3 x = 3 - 2 x = 1$

03

Step 3. Check the answer

Put $x = 1$ in given equation,

$4^{x + 2} = 64 4^{1 + 2} = 64 4^{3} = 64 64 = 64$

True

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