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 $y = 4$.

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.