54.4\:-\left(8.314\:×307.65\:\right)/\left(96485.3\:\right)×ln⁡\left(10^{\left(-6\right)}\right)=

asked by guest
on Nov 19, 2024 at 3:12 pm



You asked:

Evaluate the expression: \(54.4 - \frac{8.314 \cdot 307.65}{96485.3} \cdot \ln\left( {10}^{-6} \right)\)

MathBot Answer:

\[54.4 - \frac{8.314 \cdot 307.65}{96485.3} \cdot \ln\left( {10}^{-6} \right) = \frac{25578021 \log{\left(1000000 \right)}}{964853000} + \frac{272}{5} \approx 54.76624586250686054796391709289853\]

\[\begin{aligned}54.4 - \frac{8.314 \cdot 307.65}{96485.3} \cdot \ln\left( {10}^{-6} \right)& = 54 + \frac{4}{10} - \left(8 + \frac{314}{1000}\right) \cdot \left(307 + \frac{65}{100}\right) \cdot \frac{1}{96485 + \frac{3}{10}} \cdot \log{\left(\frac{1}{10^{6}} \right)}\\& = 54 + \frac{2}{5} - \left(8 + \frac{314}{1000}\right) \cdot \left(307 + \frac{65}{100}\right) \cdot \frac{1}{96485 + \frac{3}{10}} \cdot \log{\left(\frac{1}{10^{6}} \right)}\\& = 54 + \frac{2}{5} - \left(8 + \frac{157}{500}\right) \cdot \left(307 + \frac{65}{100}\right) \cdot \frac{1}{96485 + \frac{3}{10}} \cdot \log{\left(\frac{1}{10^{6}} \right)}\\& = 54 + \frac{2}{5} - \frac{4157}{500} \cdot \left(307 + \frac{65}{100}\right) \cdot \frac{1}{96485 + \frac{3}{10}} \cdot \log{\left(\frac{1}{10^{6}} \right)}\\& = 54 + \frac{2}{5} - \frac{4157}{500} \cdot \left(307 + \frac{13}{20}\right) \cdot \frac{1}{96485 + \frac{3}{10}} \cdot \log{\left(\frac{1}{10^{6}} \right)}\\& = 54 + \frac{2}{5} - \frac{4157}{500} \cdot \frac{6153}{20} \cdot \frac{1}{96485 + \frac{3}{10}} \cdot \log{\left(\frac{1}{10^{6}} \right)}\\& = 54 + \frac{2}{5} - \frac{4157}{500} \cdot \frac{6153}{20} \cdot \frac{1}{\frac{964853}{10}} \cdot \log{\left(\frac{1}{10^{6}} \right)}\\& = 54 + \frac{2}{5} - \frac{4157}{500} \cdot \frac{6153}{20} \cdot \frac{10}{964853} \cdot \log{\left(\frac{1}{10^{6}} \right)}\\& = 54 + \frac{2}{5} - \frac{4157}{500} \cdot \frac{6153}{20} \cdot \frac{10}{964853} \cdot \log{\left(\frac{1}{1000000} \right)}\\& = 54 + \frac{2}{5} - \frac{4157}{500} \cdot \frac{6153}{20} \cdot \frac{10}{964853} \cdot - \log{\left(1000000 \right)}\\& = 54 + \frac{2}{5} - \frac{25578021}{10000} \cdot \frac{10}{964853} \cdot - \log{\left(1000000 \right)}\\& = 54 + \frac{2}{5} - \frac{25578021}{964853000} \cdot - \log{\left(1000000 \right)}\\& = 54 + \frac{2}{5} - - \frac{25578021}{964853000} \cdot \log{\left(1000000 \right)}\\& = 54 + \frac{2}{5} + \frac{25578021}{964853000} \cdot \log{\left(1000000 \right)}\\& = \frac{272}{5} + \frac{25578021}{964853000} \cdot \log{\left(1000000 \right)}\end{aligned}\]

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