Question

antilog [ log 4 + log π + 3log r - log 3 ] ( take π = 3.142 and r = 1.273 )​

Answer 1

Answer:

Properties of logarithm used :

$log(a) + log(b) = log(ab) \\ log(a ) - log(b) = log( \frac{a}{b} ) \\ log( {a}^{m} ) = m \: log(a) \\ antilog( log(a) ) = a$

Ok so the question is

$antilog [ log (4) + log (π )+ 3 \: log (r )- log( 3) ] \\antilog [ log (4) + log (π )+ log ( {r}^{3} )- log( 3) ] \\ antilog [ log ( \frac{4\pi {r}^{3} }{3} ) ] \\ \frac{4}{3} \pi {r}^{3}$

Now it is clear that this is the formula of surface area of a circle.

Given that

$\pi = 3.142 \\ r = 1.273$

Putting values

$\frac{4}{3} \pi {r}^{3} \\ \frac{4}{3} (3.142)( {1.273})^{3} \\ = 8.642317$

This is the answer.

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