\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: 12log⁡(10⋅8117−log⁡(10⋅174+2log⁡(10⋅53+32log⁡(10⋅17))))\frac{1}{2} \log\left( 10 \cdot \frac{81}{17} - \log\left( 10 \cdot \frac{17}{4} + 2 \log\left( 10 \cdot \frac{5}{3} + \frac{3}{2} \log\left( 10 \cdot 17 \right) \right) \right) \right)

MathBot Answer:

12log⁡(10⋅8117−log⁡(10⋅174+2log⁡(10⋅53+32log⁡(10⋅17))))=log⁡(81017−log⁡(2log⁡(3log⁡(170)2+503)+852))2≈1.88933211573799391689043773532278\frac{1}{2} \log\left( 10 \cdot \frac{81}{17} - \log\left( 10 \cdot \frac{17}{4} + 2 \log\left( 10 \cdot \frac{5}{3} + \frac{3}{2} \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

12log⁡(10⋅8117−log⁡(10⋅174+2log⁡(10⋅53+32log⁡(10⋅17))))=12⋅log⁡(10⋅8117−log⁡(10⋅174+2⋅log⁡(10⋅53+32⋅log⁡(10⋅17))))=12⋅log⁡(81017−log⁡(10⋅174+2⋅log⁡(10⋅53+32⋅log⁡(10⋅17))))=12⋅log⁡(81017−log⁡(852+2⋅log⁡(10⋅53+32⋅log⁡(10⋅17))))=12⋅log⁡(81017−log⁡(852+2⋅log⁡(503+32⋅log⁡(10⋅17))))=12⋅log⁡(81017−log⁡(852+2⋅log⁡(503+32⋅log⁡(170))))\begin{aligned}\frac{1}{2} \log\left( 10 \cdot \frac{81}{17} - \log\left( 10 \cdot \frac{17}{4} + 2 \log\left( 10 \cdot \frac{5}{3} + \frac{3}{2} \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}

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