https://file.aiquickdraw.com/mathbot/file/1727186919635dql6tevn.jpg

Let's work through the problems in the image one by one.

### Problem 1: 
\[ (2^x, 81) = (32, 3^y) \]
You are asked to find the values of \(x\) and \(y\).

Step-by-step solution:
- Compare the first parts of the pairs: \(2^x = 32\). We know that \(32 = 2^5\), so:
  \[
  2^x = 2^5 \implies x = 5
  \]
- Compare the second parts: \(81 = 3^y\). We know that \(81 = 3^4\), so:
  \[
  3^y = 3^4 \implies y = 4
  \]
Thus, the values are \(x = 5\) and \(y = 4\).

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### Problem 2:
The expression is \(10x^4 y\), and you are asked to find the literal coefficient of \(y\).

Solution:
- In the term \(10x^4 y\), the **literal coefficient** is the product of the variables (excluding the numerical coefficient). Here, the variables are \(x^4\) and \(y\), so the literal coefficient of \(y\) is:
  \[
  x^4
  \]

---

### Problem 3:
You are given the sequence:
\[ 5.9, 5.99, 5.999, \dots \]
and asked to find the nearest whole number of the sequence.

Step-by-step explanation:
- Notice that the numbers are approaching a limit. Specifically, as the number of decimal places increases, the sequence converges to 6.
- The nearest whole number for all terms in this sequence is:
  \[
  6
  \]

---

Would you like further details or have any questions?

### Related Questions:
1. How do you solve for variables in an exponential equation like \(2^x = 32\)?
2. What is the difference between literal and numerical coefficients?
3. How does one determine if a sequence converges?
4. What methods can be used to approximate the limit of a sequence?
5. Can you explain more about solving exponential equations using logarithms?

### Tip:
When comparing terms in exponential forms, always try to express both sides as powers of the same base for easier comparison.

If (2^x, 81) = (32, 3^y), find the values of x and y; In 10x^4 y, what is the literal coefficient of y? Which is the nearest whole number of the sequence 5.9, 5.99, 5.999,...?

This page explains how to solve an exponential equation like (2^x, 81) = (32, 3^y), determine the literal coefficient of y in the expression 10x^4y, and find the nearest whole number in the sequence 5.9, 5.99, 5.999. Suitable for students in Grades 8-10.

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