Chapter 5: Q. 73 (page 284)

solve each equation. Verify your results using a graphing utility.
$3^{x^{2} - 7} = 27^{2 x}$

Short Answer

Expert verified

The value of x for which the above equation is valid are :

$- 1, 7$

Step by step solution

Step 1. Given equation

$3^{x^{2} - 7} = 27^{2 x}$

Step 2. Solving exponentially

$3^{x^{2} - 7} = 27^{2 x} 3^{x^{2} - 7} = 3^{3 (2 x)} 3^{x^{2} - 7} = 3^{6 x}$

By exponential property

$a^{v} = a^{u} \Rightarrow v = u$

Using this :

$x^{2} - 6 x - 7 = 0 \Rightarrow x^{2} - 7 x + x - 7 = 0 \Rightarrow x (x - 7) + 1 (x - 7) = 0 \Rightarrow (x + 1) (x - 7) = 0 \Rightarrow x = - 1 o r x = 7$

Step 3. Verifying Graphically

Sketching the graphs of

$3^{x^{2} - 7} & 27^{2 x}$

Where they will intersect will be the solution .

They intersect at -1,7

hence verified

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solve each equation. Verify your results using a graphing utility.
$3^{x^{2} - 7} = 27^{2 x}$

Short Answer

Step by step solution

Step 1. Given equation

Step 2. Solving exponentially

Step 3. Verifying Graphically

One App. One Place for Learning.

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solve each equation. Verify your results using a graphing utility.3x2-7=272x

Short Answer

Step by step solution

Step 1. Given equation

Step 2. Solving exponentially

Step 3. Verifying Graphically

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Pure Maths

Calculus

Applied Mathematics

Logic and Functions

Geometry

Study anywhere. Anytime. Across all devices.

solve each equation. Verify your results using a graphing utility.
$3^{x^{2} - 7} = 27^{2 x}$