Question

What is the largest integer value of n for which 3^n is less than 200?

OPTION 1: 4
OPTION 2: 5
OPTION 3: 6
OPTION 4: 7

Answer 1

The largest integer value of n for which
`3^n` is less than 200 is 7.Thus the correct option is 4.

Step-by-step explanation:

To find the largest integer value of n for which
`3^n` is less than 200, we need to solve the inequality
`3^n` < 200.

Let's start by checking the powers of 3 to determine when it exceeds 200:

`3^1` = 3

3² = 9

3³ = 27

`3^4` = 81

`3^5` = 243

We can see that
`3^5` is greater than 200, so n = 5 is not the solution. Now, let's verify for n = 6:

`3^6` = 729

As
`3^6`is greater than 200, n = 6 is also not the solution. Finally, for n = 7:

`3^7` = 2187

Since
`3^7` is greater than 200, n = 7 is the first value for which
`3^n` exceeds 200. Therefore, the largest integer value of n for which
`3^n` is less than 200 is 7. To confirm, we can note that
`3^6` = 729 and
`3^7` = 2187, ensuring that
`3^7` is indeed the first value to exceed 200 while
`3^6` remains below 200. Hence, OPTION 4: 7 is the correct answer.Thus the correct option is 4.