In each of the following, find all real numbers x that satisfy the given equation. If none satisfy the equation, then state the answer as "None." a. 5* = 25 d. ³√x=2³√7 A. b. 25=3125 X = 2 e. x = 3 3x 9 (216) 25 f. (x + 1)² = 3 C. a. Select the correct answer below and, if necessary, fill in the answer box to complete your choice. O A. x= (Simplify your answer. Type exact answers, using radicals as needed. Use a comma to separate answers as needed.) B. None b. Select the correct answer below and, if necessary, fill in the answer box to complete your choice. 243 3125 (Simplify your answer. Type exact answers, using radicals as needed. Use a comma to separate answers as needed.) O B. None c. Select the correct answer below and, if necessary, fill in the answer box to complete your choice. OA. x= (Simplify your answer. Type exact answers, using radicals as needed. Use a comma to separate answers as needed.) B. None
In each of the following, find all real numbers x that satisfy the given equation. If none satisfy the equation, then state the answer as "None." a. 5* = 25 d. ³√x=2³√7 A. b. 25=3125 X = 2 e. x = 3 3x 9 (216) 25 f. (x + 1)² = 3 C. a. Select the correct answer below and, if necessary, fill in the answer box to complete your choice. O A. x= (Simplify your answer. Type exact answers, using radicals as needed. Use a comma to separate answers as needed.) B. None b. Select the correct answer below and, if necessary, fill in the answer box to complete your choice. 243 3125 (Simplify your answer. Type exact answers, using radicals as needed. Use a comma to separate answers as needed.) O B. None c. Select the correct answer below and, if necessary, fill in the answer box to complete your choice. OA. x= (Simplify your answer. Type exact answers, using radicals as needed. Use a comma to separate answers as needed.) B. None
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![### Finding Real Numbers that Satisfy the Given Equations
Below are several equations. For each, determine all real numbers \( x \) that satisfy the equation. If none satisfy the equation, select "None."
### Equations:
a. \( 5^x = 25 \)
b. \( 25^{-x} = 3125 \)
c. \( \left( \frac{9}{25} \right)^{-3x} = \frac{243}{3125} \)
d. \( \sqrt[3]{\frac{x}{7}} = 2\sqrt[3]{7} \)
e. \( x^{-\frac{2}{5}} = 3 \)
f. \( (x + 1)^2 = 3 \)
---
### Answer Sections:
#### a. Select the correct answer below and, if necessary, fill in the answer box to complete your choice.
- ☐ A. \( x = \) [__________]
(Simplify your answer. Type exact answers, using radicals as needed. Use a comma to separate answers as needed.)
- ☐ B. None
#### b. Select the correct answer below and, if necessary, fill in the answer box to complete your choice.
- ☑ A. \( x = \) [__________]
(Simplify your answer. Type exact answers, using radicals as needed. Use a comma to separate answers as needed.)
- ☐ B. None
#### c. Select the correct answer below and, if necessary, fill in the answer box to complete your choice.
- ☐ A. \( x = \) [__________]
(Simplify your answer. Type exact answers, using radicals as needed. Use a comma to separate answers as needed.)
- ☐ B. None
---
In each case, carefully calculate the value(s) of \( x \) or determine if no real values of \( x \) will satisfy the equation. Remember to consider the properties of exponents and roots when simplifying your answers.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F893c97d9-09c7-4f3e-b188-bcf1f5d21bb1%2F2e54a855-a666-4048-be15-1e3501e3bdc6%2Fbfjvo9h_processed.png&w=3840&q=75)
Transcribed Image Text:### Finding Real Numbers that Satisfy the Given Equations
Below are several equations. For each, determine all real numbers \( x \) that satisfy the equation. If none satisfy the equation, select "None."
### Equations:
a. \( 5^x = 25 \)
b. \( 25^{-x} = 3125 \)
c. \( \left( \frac{9}{25} \right)^{-3x} = \frac{243}{3125} \)
d. \( \sqrt[3]{\frac{x}{7}} = 2\sqrt[3]{7} \)
e. \( x^{-\frac{2}{5}} = 3 \)
f. \( (x + 1)^2 = 3 \)
---
### Answer Sections:
#### a. Select the correct answer below and, if necessary, fill in the answer box to complete your choice.
- ☐ A. \( x = \) [__________]
(Simplify your answer. Type exact answers, using radicals as needed. Use a comma to separate answers as needed.)
- ☐ B. None
#### b. Select the correct answer below and, if necessary, fill in the answer box to complete your choice.
- ☑ A. \( x = \) [__________]
(Simplify your answer. Type exact answers, using radicals as needed. Use a comma to separate answers as needed.)
- ☐ B. None
#### c. Select the correct answer below and, if necessary, fill in the answer box to complete your choice.
- ☐ A. \( x = \) [__________]
(Simplify your answer. Type exact answers, using radicals as needed. Use a comma to separate answers as needed.)
- ☐ B. None
---
In each case, carefully calculate the value(s) of \( x \) or determine if no real values of \( x \) will satisfy the equation. Remember to consider the properties of exponents and roots when simplifying your answers.
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