My Math Forum Calculating using logarithms

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 August 31st, 2015, 04:08 AM #1 Newbie   Joined: Aug 2014 From: Australia Posts: 2 Thanks: 0 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.
 August 31st, 2015, 04:45 AM #2 Newbie   Joined: Aug 2014 From: Australia Posts: 2 Thanks: 0 Apologies, I see why now... When adding and subtracting they need to be evaluated beforehand.

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