x^x = y means x to the power of x equals y. ^ is a common notation on computers used to mean "to the power of". x^x = y is an equation that cannot be solved in one step. You must use a method that gains accuracy every time you do it. It is very similar to Newton's method of square roots by dividing and averaging. Here is the method:

• Take y.
• Take another variable z. It equals y / 2.
• x then equals log10 (y) / log10 (z).
• log10 (y) means the logarithm to the base ten of y.
• Now assign z to equal x plus the previous value of z divided by 2.
• Or, (x + z) / 2.
• Repeat this process many times to find x accurately.

As you may have guessed, a computer program would be very useful here. Here is the source code for one in QBASIC:

• PRINT "Solving x^x"
• PRINT "-----------"
• PRINT
• INPUT "y?", y
• z = y / 2
• FOR i = 1 TO 3000
• x = LOG(y) / LOG(z)
• z = (x + z) / 2
• NEXT i
• PRINT x

You can download the executable here which is written in Visual Basic. A computer program really is required in order to get an accurate result.

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