(0.36 Log^2 0.36)-(0.64 Log^2 0.64)

asked by guest
on Nov 26, 2024 at 7:30 pm



You asked:

Evaluate the expression: \(0.36 {\log\left( 0.36 \right)}^{2} - 0.64 {\log\left( 0.64 \right)}^{2}\)

MathBot Answer:

\[0.36 {\log\left( 0.36 \right)}^{2} - 0.64 {\log\left( 0.64 \right)}^{2} = - \frac{16 \log{\left(\frac{16}{25} \right)}^{2}}{25} + \frac{9 \log{\left(\frac{9}{25} \right)}^{2}}{25} \approx 0.24828746386773494253691071421647\]

\[\begin{aligned}0.36 {\log\left( 0.36 \right)}^{2} - 0.64 {\log\left( 0.64 \right)}^{2}& = \frac{36}{100} \cdot \log{\left(\frac{36}{100} \right)}^{2} - \frac{64}{100} \cdot \log{\left(\frac{64}{100} \right)}^{2}\\& = \frac{36}{100} \cdot \log{\left(\frac{9}{25} \right)}^{2} - \frac{64}{100} \cdot \log{\left(\frac{64}{100} \right)}^{2}\\& = \frac{9}{25} \cdot \log{\left(\frac{9}{25} \right)}^{2} - \frac{64}{100} \cdot \log{\left(\frac{64}{100} \right)}^{2}\\& = \frac{9}{25} \cdot \log{\left(\frac{9}{25} \right)}^{2} - \frac{64}{100} \cdot \log{\left(\frac{16}{25} \right)}^{2}\\& = \frac{9}{25} \cdot \log{\left(\frac{9}{25} \right)}^{2} - \frac{16}{25} \cdot \log{\left(\frac{16}{25} \right)}^{2}\\& = - \frac{16}{25} \cdot \log{\left(\frac{16}{25} \right)}^{2} + \frac{9}{25} \cdot \log{\left(\frac{9}{25} \right)}^{2}\end{aligned}\]

+ Submit Question