Question

`x^x+x^7=326592` find `x`?

Answer 1

`x=6`

Explanation:

Since we have `x` raised to itself and to a number, there is no simple calculation to perform.

One way of finding the answer is an iteration method.

`x^x+x^7=326592`

`x^7=326592-x^x`

`x=(326592-x^x)^(1/7)`

Let `x_0=5`

`x_1=(326592-5^5)^(1/7)=6.125`
`x_2=(326592-6.125^6.125)^(1/7)=5.938`
`x_3=(326592-5.938^5.938)^(1/7)=6.022`
`x_4=(326592-6.022^6.022)^(1/7)=5.991`
`x_5=(326592-5.991^5.991)^(1/7)=6.004`
`x_6=(326592-6.004^6.004)^(1/7)=5.999`
`x_7=(326592-5.999^5.999)^(1/7)=6.001`
`x_8=(326592-6.001^6.001)^(1/7)=6.000`
`x_9=(326592-6.000^6.000)^(1/7)=6.000`

Though you may do yours to 1 ot two decimal places and do the first 5 iterations, giving a good approximation.