Question

determine os valores de
$f( \times ) = log \frac{ \times 2}{2}$
para:
a)f(8)
b) f(1)
c)f(1/2)
d)f(1/16)​

Answer 1

$\boxed{ f(x) = log_{10}( \frac{x {}^{2} }{2} ) }$

$a) \\ f(8) = log_{10}( \frac{8 {}^{2} }{2} ) \\ f(8) = log_{10}( \frac{64}{2} ) \\ f(8) = log_{10}(32) \\ f(8) = log_{10}(2 {}^{5} ) \\ \boxed{\boxed{\boxed{f(8) = 5 log_{10}(2) }}}$

$b) \\ f(1) = log_{10}( \frac{1 {}^{2} }{2} ) \\ f(1) = log_{10}( \frac{1}{2} ) \\ f(1) = log_{10}(2 {}^{ - 1} ) \\ \boxed{\boxed{\boxed{f(1) = - log_{10}(2) }}}$

$c) \\ f( \frac{1}{2} ) = log_{10}( \frac{( \frac{1}{2} ) {}^{2} }{2} ) \\ f( \frac{1}{2} ) = log_{10}( \frac{ \frac{1}{4} }{2} ) \\ f( \frac{1}{2} ) = log_{10}( \frac{1}{8} ) \\ f( \frac{1}{2} ) = log_{10}(2 {}^{ - 3} ) \\ \boxed{\boxed{\boxed{ f( \frac{1}{2} ) = - 3 log_{10}(2) }}}$

$d) \\ f( \frac{1}{16} ) = log_{10}( \frac{ (\frac{1}{16} ) {}^{2} }{2} ) \\ f( \frac{1}{16} ) = log_{10}( \frac{ \frac{1}{256} }{2} ) \\ f( \frac{1}{16} ) = log_{10}( \frac{1}{512} ) \\ f( \frac{1}{16} ) = log_{10}(2 {}^{- 9} ) \\\boxed{\boxed{\boxed{f( \frac{1}{16} ) = - 9 log_{10}(2) }}}$

att. yrz