Determine-the-numerical-value-of-the-following-expression-without-the-use-of-a-calculator-log-log-3-log-2-3-2sin-pi-3-pi-3-1-1-log-2-log-3-1-100-Mastermind-

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

Determine the numerical value of the

following expression without the use

of a calculator

\log [\log (3) \cdot (\log (2) \cdot (\frac{\sqrt{3} - 2 \sin (\frac{π}{3})}{π^{3} + 1} + 1)) - \log (2) \log (3) + {(- 1)}^{100}]

Mastermind

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

\log [\log (3) . (\log (2) . (\frac{\sqrt{3} - 2 \frac{\sqrt{3}}{2}}{π^{3} + 1} + 1)) - \log (2) \log (3) + 1]

= \log [\log (3) . (\log (2) - \log (2) \log (3) + 1]

= \log (1) = 0