SOLUTION: If x^x = 5, find x^x^(x+1)

Question 1209790: If x^x = 5,
find x^x^(x+1)
Found 4 solutions by CPhill, Edwin McCravy, math_tutor2020, MathTherapy:
Answer by CPhill(1959)   (Show Source): You can put this solution on YOUR website!
Given that x^x = 5, we can substitute this value into the expression we want to evaluate:
x^x^(x+1) = x^(x * x^(x+1))
Now, substitute x^x = 5:
x^(x * x^(x+1)) = x^(5 * x^(x+1))
Again, substitute x^x = 5:
x^(5 * x^(x+1)) = x^(5 * 5^(x+1))
Since we don't have an explicit value for x, we can't simplify this expression further without additional information or assumptions about x.
If you have more context or constraints on the value of x, please provide them, and I'll try to give a more specific answer.
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!

Given Edwin

Answer by math_tutor2020(3816)   (Show Source): You can put this solution on YOUR website!

Answer: 3125

Work Shown
x^( x^(x+1) )
= x^( x^x*x^1 )
= x^( x^x*x^1 )
= x^(5x) ............. plug in x^x = 5
= (x^x)^5
= 5^5
= 3125

To help verify this answer, we could graph y = (x^x)-5.
I recommend either Desmos or GeoGebra as a graphing calculator.
The approximate x intercept is roughly x = 2.1293724828
x^x = 2.1293724828^2.1293724828 = 5.00000000035 approximately which is really close to 5.
Then,
w = x^(x+1) = 2.1293724828^(2.1293724828+1) = 10.64686241474 approximately
and
x^w = 2.1293724828^10.64686241474 = 3125.000002841
While we don't land on exactly 3125 like we should, it's fairly close. If you used more decimal digits then you should get even closer to the answer.

Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!

If x^x = 5, find x^x^(x+1) --- Applying ------- Substituting 5 for ------- Applying ------- Applying Substituting 5 for , we get:

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