# Raising a whole number to a fractional power

Abel 11:27 14 Sep 2004
Locked

While I understand the principle of raising numbers to a power I'm having great difficulty in raising a whole number to the power of a fraction eg £1,723.50 to the power of 18/365ths.

Please make any explanation as simple as possible because my mathmatical education leaves to be desired.

Abel

jbaker65 11:36 14 Sep 2004

The easiest way is to take the logarithm of the number, multiply it by the numerator of the power, divide by the denominator of the power and then take the anti-log. In your example, the log of 1823.5 is 3.2609058. Multiply this by 18=58.696304. Divide by 365=0.1608117. Now take anti-log=1.4481441 and that is your answer.

Pesala 11:39 14 Sep 2004

(~_~)

Sans le Sou 11:45 14 Sep 2004

Its 85 quid.

Sans le Sou 12:02 14 Sep 2004

like this log10, 1723.5 = 3.2364113 + log10, 18(1.2552725) = 4.4916838 - log10,365 (2.5622929) = 1.9293909. antilog of 1.9293909 = 84.99452 or 85 to 2 sig figs.

QED

or you can just multiply 1723.5 times 0.049315

or buy a calculator!

Abel 12:19 14 Sep 2004

Smart a**'* like Pesala and Sans le Sou this world can do without. However, many thanks jbaker65.

Abel

Sans le Sou 12:27 14 Sep 2004

Not really, when I was at school the calculator had not been invented. We spent years doing all calculations with "Uncle Napier's" log and other mathematical tables or a sliderule.Took bloody hours doing some calculations, decent calculator does same sums in seconds these days. So sorry to have been damaged by a State Grammar School education.

jbaker65 15:32 14 Sep 2004

Sans le Sou, I too learnt maths before calculators (I'm 76 now) but I must point out that the solution you gave was mathmatically incorrect. I am sure you realised this afterwards.

Sans le Sou 12:19 15 Sep 2004

Perhaps you can point it out probably 2 sig figs was it? You can only add or subtract log numbers to multiply or divide proper numbers, I think you are in error when you multiply a number converted to logs by a proper number. You also started with the wrong amount of 1823.5. Why am I explaining this........ I must be ready for the men in white coats!!

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