Question

How to find x, `x^5=9`?

`x^5=9`

Answer 1

`x = root5(9) = 1.5518...`

Explanation:

Apply the same principles as with other equations....

You want to isolate `x` on the left.

Whatever you do on the left you must do on the right,

To get rid of the `5th` power, find the `5th` root.

`x^5 =9`

`root5(x^5) = root5(9)`

`x= root5(9)`

This is an irrational number, but using a calculator will give you:

`x = 1.5518..`

If you estimate an answer this seems right.

`1^5 = 1" "and" "2^5 = 32`

Therefore `9` has to be `1` raised to `1.??????`

`1^1.5518 =9`

Answer 2

Another approach option

`x~~1.5518` to 4 decimal places

Explanation:

Uses what they now call log inverse. Way, way back when I was at school they called them 'antilogs'. It reverses the process of taking a log so that you end up at the source number.

Given: `x^5=9`

Taking logs of both sides. I chose log to base 10

`log_10(x^5)=log_10(9)`

`5log_10(x)=log_10(9)`

`log_10(x)=log_10(9)/5`

`x=log_10color(white)()^(-1)(( log_10(9))/5)`

`x=1.5518455......`

`x~~1.5518` to 4 decimal places