\frac{1}{2} \log{10}\left(\frac{81}{17}\right) - \log{10}\left(\frac{17}{4}\right) + 2 \log{10}\left(\frac{5}{3}\right) + \frac{3}{2} \log{10}(17)

asked by guest
on Nov 22, 2024 at 8:56 am



You asked:

Evaluate the expression: \(\frac{1}{2} \cdot \log\left( 10 \cdot \frac{81}{17} - \log\left( 10 \cdot \frac{17}{4} + 2 \cdot \log\left( 10 \cdot \frac{5}{3} + \frac{3}{2} \cdot \log\left( 10 \cdot 17 \right) \right) \right) \right)\)

MathBot Answer:

\[\frac{1}{2} \cdot \log\left( 10 \cdot \frac{81}{17} - \log\left( 10 \cdot \frac{17}{4} + 2 \cdot \log\left( 10 \cdot \frac{5}{3} + \frac{3}{2} \cdot \log\left( 10 \cdot 17 \right) \right) \right) \right) = \frac{\log{\left(\frac{810}{17} - \log{\left(2 \log{\left(\frac{3 \log{\left(170 \right)}}{2} + \frac{50}{3} \right)} + \frac{85}{2} \right)} \right)}}{2} \approx 1.88933211573799391689043773532278\]


\[\begin{aligned}\frac{1}{2} \cdot \log\left( 10 \cdot \frac{81}{17} - \log\left( 10 \cdot \frac{17}{4} + 2 \cdot \log\left( 10 \cdot \frac{5}{3} + \frac{3}{2} \cdot \log\left( 10 \cdot 17 \right) \right) \right) \right)& = \frac{1}{2} \cdot \log{\left(10 \cdot \frac{81}{17} - \log{\left(10 \cdot \frac{17}{4} + 2 \cdot \log{\left(10 \cdot \frac{5}{3} + \frac{3}{2} \cdot \log{\left(10 \cdot 17 \right)} \right)} \right)} \right)}\\& = \frac{1}{2} \cdot \log{\left(\frac{810}{17} - \log{\left(10 \cdot \frac{17}{4} + 2 \cdot \log{\left(10 \cdot \frac{5}{3} + \frac{3}{2} \cdot \log{\left(10 \cdot 17 \right)} \right)} \right)} \right)}\\& = \frac{1}{2} \cdot \log{\left(\frac{810}{17} - \log{\left(\frac{85}{2} + 2 \cdot \log{\left(10 \cdot \frac{5}{3} + \frac{3}{2} \cdot \log{\left(10 \cdot 17 \right)} \right)} \right)} \right)}\\& = \frac{1}{2} \cdot \log{\left(\frac{810}{17} - \log{\left(\frac{85}{2} + 2 \cdot \log{\left(\frac{50}{3} + \frac{3}{2} \cdot \log{\left(10 \cdot 17 \right)} \right)} \right)} \right)}\\& = \frac{1}{2} \cdot \log{\left(\frac{810}{17} - \log{\left(\frac{85}{2} + 2 \cdot \log{\left(\frac{50}{3} + \frac{3}{2} \cdot \log{\left(170 \right)} \right)} \right)} \right)}\end{aligned}\]