For what positive integer n is 2n+3n+4n=nn?

divide both sides by n

2+3+4=n

To find the value of n for which the equation 2n + 3n + 4n = nn is true, we need to simplify the equation and solve for n.

First, let's simplify the left side of the equation by combining like terms:

2n + 3n + 4n = nn

(2 + 3 + 4) n = nn

9n = nn

Now, we can solve this equation by considering different cases:

Case 1: n = 0
Substituting n = 0 into the equation, we get:

9(0) = (0)(0)
0 = 0

Since this is true, n = 0 is a solution.

Case 2: n ≠ 0
In this case, we can divide both sides of the equation by n:

9 = n

So, for n ≠ 0, the solution is n = 9.

Therefore, the positive integer value of n that satisfies the equation 2n + 3n + 4n = nn is n = 9.

To find the positive integer value of n that satisfies the equation 2n + 3n + 4n = nn, we can start by simplifying the equation on the left-hand side:

2n + 3n + 4n = nn

Adding like terms, we get:

9n = nn

Next, we can rearrange the equation to isolate n on one side:

nn - 9n = 0

Factoring out n, we have:

n(n - 9) = 0

This equation can be satisfied if either n = 0 or n - 9 = 0. However, we are looking for positive integer values of n, so we can only consider n - 9 = 0.

Solving n - 9 = 0, we find:

n = 9

Therefore, the positive integer value of n that satisfies the equation 2n + 3n + 4n = nn is n = 9.