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Solving equations such as 7x=343
By Thomas Coton on Monday, October 07, 2002 - 08:45 pm:

Does anyone know if there is an easy (ish) way of doing things like 7x=343, that a year 9 can understand?

Thomas

By David Loeffler on Monday, October 07, 2002 - 09:05 pm:

I remember I asked my maths teacher exactly the same question when I was in year 9! He entirely failed to make me understand the answer, so let's see if I can do any better for you.

The answer is to use something called a logarithm. This is a special function which has the property that log(ab) = log a + log b, and log(ab) = b log a.

Thus in your example, we have:
7x = 343
log(7x) = log 343
x log 7 = log 343
x = log 343 / log 7

Now, there are lots of sorts of logarithms - we say there are logarithms to different bases. But in the above calculation it doesn't matter what base you use so long as you use the same base throughout.

A lot of calculators have a button marked 'log' which generates logarithms to base 10. If that's the case on your calculator, you should find it gives log 343 = 2.53529412, and log 7 = 0.84509804. And, of course, 2.53429412 / 0.84509804 = 3, which is the answer.

(This is a very simple method if you have a calculator handy, but I haven't told you how to calculate a logarithm by hand. It's really not at all easy, I'm afraid.)

David

By Thomas Coton on Monday, October 07, 2002 - 09:08 pm:

Thanks a lot, David. I'll try it.

Thomas

By Sam Hughes on Friday, October 11, 2002 - 06:58 pm:

Alternatively, put 1 in your calculator and multiply by 7, then by 7 again and again until you reach 343, counting the number of times you hit "=".

By Marcos Charalambides on Saturday, October 12, 2002 - 08:03 am:

Of course Sam's idea won't work for something like:
3x = 25
and if you don't use the log function on your calculator you'll have to use trial and error...

By Thomas Coton on Monday, November 04, 2002 - 03:49 pm:

No! No! Anything but that!