(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: 0.36log⁡(0.36)2−0.64log⁡(0.64)20.36 {\log\left( 0.36 \right)}^{2} - 0.64 {\log\left( 0.64 \right)}^{2}

MathBot Answer:

0.36log⁡(0.36)2−0.64log⁡(0.64)2=−16log⁡(1625)225+9log⁡(925)225≈0.248287463867734942536910714216470.36 {\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

0.36log⁡(0.36)2−0.64log⁡(0.64)2=36100⋅log⁡(36100)2−64100⋅log⁡(64100)2=36100⋅log⁡(925)2−64100⋅log⁡(64100)2=925⋅log⁡(925)2−64100⋅log⁡(64100)2=925⋅log⁡(925)2−64100⋅log⁡(1625)2=925⋅log⁡(925)2−1625⋅log⁡(1625)2=−1625⋅log⁡(1625)2+925⋅log⁡(925)2\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