Question

Calcule a soma S nesse caso:
a) S=log100 0,1+log25 ∛5+ log√2²

Answer 1

$Resolu\c{c}\~ao\to \left\{\begin{array}{ccc}S = log_{100}\ 0,1+log_{25}\ \sqrt[3]{5} + log_{ \sqrt{2}}\ 2 \\\\log_{100}\ 0,1 = x\\100^x = 0,1\\10^{2x} = 10^{-1}\\\boxed{x = - \frac{1}{2}}\\\\ log_{25}\ \sqrt[3]{5} = x\\25^x = \sqrt[3]{5}\\5^{2x} = 5^{ \frac{1}{3} }\\\boxed{x = \frac{1}{6} }\\\\ log_{ \sqrt{2} }\ 2 = x\\( \sqrt{2} )^x = 2\\2^{ \frac{x}{2} } = 1\\\boxed{x = 2}\\\\S = - \frac{1}{2}+ \frac{1}{6}+2 = \frac{-3+1+12}{6} = \frac{10}{6} = \boxed{\frac{5}{4}} \end{array}\right$

Espero ter ajudado. :))