Can anyone help with: x^6 = .9?

Question

(Solve for x)

Answer 1

Nowadays, we use the computers to take the 6th root of a number like 0.9 to get the answer. You can use Excel as follows:

Formula for nth Root in Excel

The following is the general form of the equation

=num^(1/n)

where "num" is the number you want to find the root of and "n" is the root.

So, you have to write in excel    = 0.9^(1/6)   to get the value of x

Earlier, people use to use logaritmic tables to  find out in the following manner:

x^6= 0.9 , or, 8*logx= log (0.9) or log x = log0.9/6

Now consult the log table to find the value of log0.9

Then divide the value of lo0.9 by 6. Then take the antilog of that value to get the value of x.

are lots of ways to find logarithms without a calculator. After all, people had to do this when there were no calculators.

1. Logarithm tables are in books and all over the place. Here is an example of a log table on the internet:

http://www.sosmath.com/tables/logtable/l...

2. My advisor in graduate school actually memorized a lot of values from the log tables so he could do very fast mental calculations.

3. Slide rules are easy ways to get approximate logarithm values.

4. There are numerical methods for approximating logarithms that you can track down, for various values of the argument. For example, look at

http://www.maths.abdn.ac.uk/~igc/tch/ma1...

http://mathworld.wolfram.com/NaturalLoga...

http://www.informatik.tu-darmstadt.de/ft...

Answer 2

X=0.98259319385268986192379046116975

(0.982593193852689861923790461)^6=0.9