Question

If x^x^x=(x*x)^x
then x is equal to
1

Answer 1

Answer:

Solve for x by simplifying both sides of the equation, then isolating the variable. x ≈ 0.34632336 , 1 , 2

Step-by-step explanation:

Answer 2

Note: For the actual answer, refer to the 2nd part.

Step-by-step explanation:

1st part:

x^x^x = (x•x)^x

x^(x²) = x²^x

x^(x²) = x^(2x) (Law of indices)

x² = 2x (Taking log with base x)

x² - 2x = 0

x (x - 2) = 0

x = 0 or (x - 2) = 0

x = 0 or x = 2

But 0^0 is undefined.

x ≠ 0

x = 2

2nd part:

Let us solve the equation with x = 1. That would be the proof to your question.

Hope that helps you....

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