Match the exропent equality to the correсt solution for x. 1. 27*-3 3* а. х — —4 2. 5-5 = 5 b. х — — 6 3 С. — 2 3. 16*+2 = 4ª-2 4. 25*+3 5+2 d. x = 6 ||
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
![### Matching Exponent Equations to Solutions
To enhance your understanding of exponent equations, let's go through the following matching exercise. Match each given exponent equality with its corresponding solution for \( x \):
1. \( 27^{x-3} = 3^x \)
2. \( 5^{x-5} = 5 \)
3. \( 16^{x+2} = 4^{x-2} \)
4. \( 25^{x+3} = 5^{x+2} \)
**Possible Solutions:**
a. \( x = -4 \)
b. \( x = -6 \)
c. \( x = \frac{3}{2} \)
d. \( x = 6 \)
### Instructions
Match each equation to the correct value of \( x \) from the provided list:
1. \( 27^{x-3} = 3^x \) matches with ______.
2. \( 5^{x-5} = 5 \) matches with ______.
3. \( 16^{x+2} = 4^{x-2} \) matches with ______.
4. \( 25^{x+3} = 5^{x+2} \) matches with ______.
### Graph Explanations
There are no graphs or diagrams included in this exercise, but working carefully through each equation will help find the correct matching of the exponent equations to the solutions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F098f8e04-469a-4a6a-8094-b45e233f0633%2Fdfce0a03-c6ff-4ac6-b518-2b47d0411cc4%2Fx78khvs_processed.jpeg&w=3840&q=75)
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