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August 31st, 2015, 04:08 AM   #1
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Calculating using logarithms

Hi all,

I have tried several methods for calculating a value using a formula with logarithms and I get varying answers depending on how I calculate it. I am leaning towards calculating the formula each time and subtracting the difference.

This is the formula:

\[\log y = 0.8 - 4.1 \times {10^{ - 4}}{\left( {8 + \log (x)} \right)^3}\]

Now I need to find the difference between x=15 and x=320, so I have tried:

\[{10^{\log \left( {\frac{{0.8 - 4.1 \times {{10}^{ - 4}}{{\left( {8 + \log (15)} \right)}^3}}}{{0.8 - 4.1 \times {{10}^{ - 4}}{{\left( {8 + \log (320)} \right)}^3}}}} \right)}}\]

and:

\[{10^{((0.8 - 4.1 \times {{10}^{ - 4}}{{\left( {8 + \log (15)} \right)}^3}) - (0.8 - 4.1 \times {{10}^{ - 4}}{{\left( {8 + \log (320)} \right)}^3}))}}\]

and:

\[{10^{(0.8 - 4.1 \times {{10}^{ - 4}}{{\left( {8 + \log (15)} \right)}^3})}} - {10^{(0.8 - 4.1 \times {{10}^{ - 4}}{{\left( {8 + \log (320)} \right)}^3})}}\]

Each time I get a different answer. I'm guessing the last method is the right one, but why do the others produce different results?

Thanks in advance.
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August 31st, 2015, 04:45 AM   #2
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Apologies, I see why now... When adding and subtracting they need to be evaluated beforehand.
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