=[1/(1-2.257)][ln (0.236/0.0783)+ 2.257ln((1-0.236)/(1-0.0783))]

asked by guest
on Mar 31, 2025 at 1:51 pm



You asked:

Evaluate the expression: 11−2.257(ln⁡(0.2360.0783)+2.257ln⁡(1−0.2361−0.0783))\frac{1}{1 - 2.257} \left(\ln\left( \frac{0.236}{0.0783} \right) + 2.257 \ln\left( \frac{1 - 0.236}{1 - 0.0783} \right)\right)

MathBot Answer:

11−2.257(ln⁡(0.2360.0783)+2.257ln⁡(1−0.2361−0.0783))=−1000log⁡(2360783)1257−2257log⁡(76409217)1257≈−0.54077456952390638963504929752404\frac{1}{1 - 2.257} \left(\ln\left( \frac{0.236}{0.0783} \right) + 2.257 \ln\left( \frac{1 - 0.236}{1 - 0.0783} \right)\right) = - \frac{1000 \log{\left(\frac{2360}{783} \right)}}{1257} - \frac{2257 \log{\left(\frac{7640}{9217} \right)}}{1257} \approx -0.54077456952390638963504929752404

11−2.257(ln⁡(0.2360.0783)+2.257ln⁡(1−0.2361−0.0783))=11−(2+2571000)⋅(log⁡(2361000⋅178310000)+(2+2571000)⋅log⁡((1−2361000)⋅11−78310000))=11−22571000⋅(log⁡(2361000⋅178310000)+(2+2571000)⋅log⁡((1−2361000)⋅11−78310000))=1−12571000⋅(log⁡(2361000⋅178310000)+(2+2571000)⋅log⁡((1−2361000)⋅11−78310000))=−10001257⋅(log⁡(2361000⋅178310000)+(2+2571000)⋅log⁡((1−2361000)⋅11−78310000))=−10001257⋅(log⁡(236⋅10783)+(2+2571000)⋅log⁡((1−2361000)⋅11−78310000))=−10001257⋅(log⁡(2360783)+(2+2571000)⋅log⁡((1−2361000)⋅11−78310000))=−10001257⋅(log⁡(2360783)+22571000⋅log⁡((1−2361000)⋅11−78310000))=−10001257⋅(log⁡(2360783)+22571000⋅log⁡((1−59250)⋅11−78310000))=−10001257⋅(log⁡(2360783)+22571000⋅log⁡(191250⋅11−78310000))=−10001257⋅(log⁡(2360783)+22571000⋅log⁡(191250⋅1921710000))=−10001257⋅(log⁡(2360783)+22571000⋅log⁡(76409217))=−10001257⋅(22571000⋅log⁡(76409217)+log⁡(2360783))=−22571257⋅log⁡(76409217)−10001257⋅log⁡(2360783)\begin{aligned}\frac{1}{1 - 2.257} \left(\ln\left( \frac{0.236}{0.0783} \right) + 2.257 \ln\left( \frac{1 - 0.236}{1 - 0.0783} \right)\right)&=\frac{1}{1 - \left(2 + \frac{257}{1000}\right)} \cdot \left(\log{\left(\frac{236}{1000} \cdot \frac{1}{\frac{783}{10000}} \right)} + \left(2 + \frac{257}{1000}\right) \cdot \log{\left(\left(1 - \frac{236}{1000}\right) \cdot \frac{1}{1 - \frac{783}{10000}} \right)}\right)\\&=\frac{1}{1 - \frac{2257}{1000}} \cdot \left(\log{\left(\frac{236}{1000} \cdot \frac{1}{\frac{783}{10000}} \right)} + \left(2 + \frac{257}{1000}\right) \cdot \log{\left(\left(1 - \frac{236}{1000}\right) \cdot \frac{1}{1 - \frac{783}{10000}} \right)}\right)\\&=\frac{1}{- \frac{1257}{1000}} \cdot \left(\log{\left(\frac{236}{1000} \cdot \frac{1}{\frac{783}{10000}} \right)} + \left(2 + \frac{257}{1000}\right) \cdot \log{\left(\left(1 - \frac{236}{1000}\right) \cdot \frac{1}{1 - \frac{783}{10000}} \right)}\right)\\&=- \frac{1000}{1257} \cdot \left(\log{\left(\frac{236}{1000} \cdot \frac{1}{\frac{783}{10000}} \right)} + \left(2 + \frac{257}{1000}\right) \cdot \log{\left(\left(1 - \frac{236}{1000}\right) \cdot \frac{1}{1 - \frac{783}{10000}} \right)}\right)\\&=- \frac{1000}{1257} \cdot \left(\log{\left(236 \cdot \frac{10}{783} \right)} + \left(2 + \frac{257}{1000}\right) \cdot \log{\left(\left(1 - \frac{236}{1000}\right) \cdot \frac{1}{1 - \frac{783}{10000}} \right)}\right)\\&=- \frac{1000}{1257} \cdot \left(\log{\left(\frac{2360}{783} \right)} + \left(2 + \frac{257}{1000}\right) \cdot \log{\left(\left(1 - \frac{236}{1000}\right) \cdot \frac{1}{1 - \frac{783}{10000}} \right)}\right)\\&=- \frac{1000}{1257} \cdot \left(\log{\left(\frac{2360}{783} \right)} + \frac{2257}{1000} \cdot \log{\left(\left(1 - \frac{236}{1000}\right) \cdot \frac{1}{1 - \frac{783}{10000}} \right)}\right)\\&=- \frac{1000}{1257} \cdot \left(\log{\left(\frac{2360}{783} \right)} + \frac{2257}{1000} \cdot \log{\left(\left(1 - \frac{59}{250}\right) \cdot \frac{1}{1 - \frac{783}{10000}} \right)}\right)\\&=- \frac{1000}{1257} \cdot \left(\log{\left(\frac{2360}{783} \right)} + \frac{2257}{1000} \cdot \log{\left(\frac{191}{250} \cdot \frac{1}{1 - \frac{783}{10000}} \right)}\right)\\&=- \frac{1000}{1257} \cdot \left(\log{\left(\frac{2360}{783} \right)} + \frac{2257}{1000} \cdot \log{\left(\frac{191}{250} \cdot \frac{1}{\frac{9217}{10000}} \right)}\right)\\&=- \frac{1000}{1257} \cdot \left(\log{\left(\frac{2360}{783} \right)} + \frac{2257}{1000} \cdot \log{\left(\frac{7640}{9217} \right)}\right)\\&=- \frac{1000}{1257} \cdot \left(\frac{2257}{1000} \cdot \log{\left(\frac{7640}{9217} \right)} + \log{\left(\frac{2360}{783} \right)}\right)\\&=- \frac{2257}{1257} \cdot \log{\left(\frac{7640}{9217} \right)} - \frac{1000}{1257} \cdot \log{\left(\frac{2360}{783} \right)}\end{aligned}

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