−(3⋅0.1log

2

(0.1)+3⋅0.15log

2

(0.15)+2⋅0.125log

2

(0.125))

asked by guest
on Nov 24, 2024 at 7:54 am



You asked:

Evaluate the expression: \(-\left( 3 \cdot 0.1 \log\left( 2 \right) \cdot 0.1 + 3 \cdot 0.15 \log\left( 2 \right) \cdot 0.15 + 2 \cdot 0.125 \log\left( 2 \right) \cdot 0.125 \right)\)

MathBot Answer:

\[-\left( 3 \cdot 0.1 \log\left( 2 \right) \cdot 0.1 + 3 \cdot 0.15 \log\left( 2 \right) \cdot 0.15 + 2 \cdot 0.125 \log\left( 2 \right) \cdot 0.125 \right) = - \frac{103 \log{\left(2 \right)}}{800} \approx -0.08924269949709295858746863563774\]


\[\begin{aligned}-\left( 3 \cdot 0.1 \log\left( 2 \right) \cdot 0.1 + 3 \cdot 0.15 \log\left( 2 \right) \cdot 0.15 + 2 \cdot 0.125 \log\left( 2 \right) \cdot 0.125 \right)& = - \left(3 \cdot \frac{1}{10} \cdot \log{\left(2 \right)} \cdot \frac{1}{10} + 3 \cdot \frac{15}{100} \cdot \log{\left(2 \right)} \cdot \frac{15}{100} + 2 \cdot \frac{125}{1000} \cdot \log{\left(2 \right)} \cdot \frac{125}{1000}\right)\\& = - \left(\frac{3}{10} \cdot \log{\left(2 \right)} \cdot \frac{1}{10} + 3 \cdot \frac{15}{100} \cdot \log{\left(2 \right)} \cdot \frac{15}{100} + 2 \cdot \frac{125}{1000} \cdot \log{\left(2 \right)} \cdot \frac{125}{1000}\right)\\& = - \left(\frac{3}{100} \cdot \log{\left(2 \right)} + 3 \cdot \frac{15}{100} \cdot \log{\left(2 \right)} \cdot \frac{15}{100} + 2 \cdot \frac{125}{1000} \cdot \log{\left(2 \right)} \cdot \frac{125}{1000}\right)\\& = - \left(\frac{3}{100} \cdot \log{\left(2 \right)} + \frac{45}{100} \cdot \log{\left(2 \right)} \cdot \frac{15}{100} + 2 \cdot \frac{125}{1000} \cdot \log{\left(2 \right)} \cdot \frac{125}{1000}\right)\\& = - \left(\frac{3}{100} \cdot \log{\left(2 \right)} + \frac{9}{20} \cdot \log{\left(2 \right)} \cdot \frac{15}{100} + 2 \cdot \frac{125}{1000} \cdot \log{\left(2 \right)} \cdot \frac{125}{1000}\right)\\& = - \left(\frac{3}{100} \cdot \log{\left(2 \right)} + \frac{27}{4} \cdot \log{\left(2 \right)} \cdot \frac{1}{100} + 2 \cdot \frac{125}{1000} \cdot \log{\left(2 \right)} \cdot \frac{125}{1000}\right)\\& = - \left(\frac{3}{100} \cdot \log{\left(2 \right)} + \frac{27}{400} \cdot \log{\left(2 \right)} + 2 \cdot \frac{125}{1000} \cdot \log{\left(2 \right)} \cdot \frac{125}{1000}\right)\\& = - \left(\frac{3}{100} \cdot \log{\left(2 \right)} + \frac{27}{400} \cdot \log{\left(2 \right)} + \frac{250}{1000} \cdot \log{\left(2 \right)} \cdot \frac{125}{1000}\right)\\& = - \left(\frac{3}{100} \cdot \log{\left(2 \right)} + \frac{27}{400} \cdot \log{\left(2 \right)} + \frac{1}{4} \cdot \log{\left(2 \right)} \cdot \frac{125}{1000}\right)\\& = - \left(\frac{3}{100} \cdot \log{\left(2 \right)} + \frac{27}{400} \cdot \log{\left(2 \right)} + \frac{125}{4} \cdot \log{\left(2 \right)} \cdot \frac{1}{1000}\right)\\& = - \left(\frac{3}{100} \cdot \log{\left(2 \right)} + \frac{27}{400} \cdot \log{\left(2 \right)} + \frac{1}{32} \cdot \log{\left(2 \right)}\right)\\& = - \left(\frac{39}{400} \cdot \log{\left(2 \right)} + \frac{1}{32} \cdot \log{\left(2 \right)}\right)\\& = - \frac{103}{800} \cdot \log{\left(2 \right)}\end{aligned}\]