# Question #da32c

##### 2 Answers

#### Explanation:

To 'get rid' of the eighths power we need to take the 8th root.

Another approach would be to use binomial expansion. I am not going to do that.

The technique I am about to use crops up every now and then. So it is useful to know.

Note that the general case of

Also reversing the process of a log is written

In the 'old days' they were called an 'antilog'.

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Divide both sides by 2

As a check: taking repeated square roots of 6 negating it and subtracting 8, I approximate the solution should be of the order:

-9.11849.......

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Taking logs of both sides

The difference between the two answers is:

Rounding errors in the calculator would contribute to the difference.

Only starting off the calculation using binomial expansion. Lot of work! You may continue on if you desire!! :-)

Good luck!

#### Explanation:

Consider only the

This one is basically a memory feat.

Standardised case going to use

In this case we start with

I am not going to write all that lot out!

Using Pascal's triangle we have:

Now you substitute for