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Question Number 174507 by Mastermind last updated on 02/Aug/22

$$\mathrm{Determine}\mathrm{the}\mathrm{numerical}\mathrm{value}\mathrm{of}\mathrm{the}$$$$\mathrm{following}\mathrm{expression}\mathrm{without}\mathrm{the}\mathrm{use}$$$$\mathrm{of}\mathrm{a}\mathrm{calculator}$$$$\log [\log \left(3\right)\cdot (\log \left(2\right)\cdot (\frac{\sqrt{3}-2\sin \left(\frac{\pi }{3}\right)}{{\pi }^3+1}+1))-\log \left(2\right)\log \left(3\right)+{(-1)}^{100}]$$$$$$$$\mathrm{Mastermind}$$

Answered by a.lgnaoui last updated on 03/Aug/22

$$\log [\log \left(3\right).(\log \left(2\right).(\frac{\sqrt{3}-2\frac{\sqrt{3}}{2}}{{\pi }^3+1}+1))-\log \left(2\right)\log \left(3\right)+1]$$$$=\log [\log \left(3\right).(\log \left(2\right)-\log \left(2\right)\log \left(3\right)+1]$$$$=\log \left(1\right)=0$$

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