Chapter 5: Q. 74 (page 284)

solve each equation. Verify your results using a graphing utility.
$5^{x^{2} + 8} = 125^{2 x}$

Short Answer

Expert verified

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

$2, 4$

Step by step solution

Step 1. Given equation

$5^{x^{2} + 8} = 125^{2 x}$

Step 2. Solving exponentially

$5^{x^{2} + 8} = 125^{2 x} 5^{x^{2} + 8} = 5^{3 (2 x)} 5^{x^{2} + 8} = 5^{6 x}$

By exponential property

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

Using this :

$x^{2} + 8 = 6 x \Rightarrow x^{2} - 6 x + 8 = 0 \Rightarrow x^{2} - 4 x - 2 x + 8 = 0 \Rightarrow x (x - 4) - 2 (x - 4) = 0 \Rightarrow (x - 2) (x - 4) = 0 \Rightarrow x = 2 o r x = 4$

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solve each equation. Verify your results using a graphing utility.
$5^{x^{2} + 8} = 125^{2 x}$

Short Answer

Step by step solution

Step 1. Given equation

Step 2. Solving exponentially

One App. One Place for Learning.

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solve each equation. Verify your results using a graphing utility.5x2+8=1252x

Short Answer

Step by step solution

Step 1. Given equation

Step 2. Solving exponentially

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Logic and Functions

Calculus

Pure Maths

Mechanics Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

solve each equation. Verify your results using a graphing utility.
$5^{x^{2} + 8} = 125^{2 x}$