Question

Determine the numerical value of the following expression without the use of a calculator:

Answer 1

Answer:3

Step-by-step explanation: Don't know

Answer 2

The numerical value if the expression is 0

The expression to be solved is

$log ( log ( 3 )- log ( 2 ) - (\frac{\sqrt{3}-2sin ( \frac{pi}{3} ) }{pi^{3} +1 } +1)) - log ( 2 ) log ( 3) } + ( -1 )^{100}$

How to solve the given expression

sin ( pi/3 ) = $\frac{\sqrt{3} }{2}$

2sin ( pi/3 ) = 2 *  $\frac{\sqrt{3} }{2}$ = $\sqrt{3}$

$log ( log ( 3 )(log ( 2 ) (\frac{\sqrt{3}-2sin ( \frac{pi}{3} ) }{pi^{3} +1 } +1)) - log ( 2 ) log ( 3) } + ( -1 )^{100})\\log ( log ( 3 ) log ( 2 ) (\frac{\sqrt{3}- \sqrt{3} }{pi^{3} +1 } +1)) - log ( 2 ) log ( 3) } + ( -1 )^{100})\\log ( log ( 3 ) log ( 2 ) (\frac{0 }{pi^{3} +1 } +1)) - log ( 2 ) log ( 3) } + ( -1 )^{100})$

$log ( log ( 3 ) log ( 2 ) (0 +1 ) - log ( 2 ) log ( 3) } + ( -1 )^{100})\\log ( log ( 3 ) log ( 2 ) - log ( 2 ) log ( 3) + ( -1 )^{100})\\log (0 + ( -1 )^{100})$

since 100 is even

$( -1 )^{100} = 1$

therefore

$log (0 + ( -1 )^{100})\\log (0 + 1)\\log 1\\0$

Read more on logarithm here: brainly.com/question/247340

#SPJ1

The complete question is attached