Question

O valor de soma S= log 10 0,0001 + log 5 √5 – log2 ∛4
é igual a:

Answer 1

Lembrando que:

logₐb = x → aˣ = b
$\sqrt[a]{x^{b} } = x^{ \frac{b}{a} }$
logₐb = $\frac{log_{c}b }{ log_{c} a}$
$log a ^{b} = b. log a$

S = log10⁻⁴ + log₅√5 - log₂$\sqrt[3]{4}$

Então:

-4 log 10 + log₅$5^{ \frac{1}{2}}$ - log₂ $\sqrt[3]{ 2^{2} }$
-4.1 + $\frac{log 5^{ \frac{1}{2} } }{log5}$ - $log_{2} 2^{ \frac{2}{3} }$
-4 + $\frac{log 5^{ \frac{1}{2} } }{log5}$ - $\frac{log 2^{ \frac{2}{3} } }{log_{2} }$
-4 + $\frac{1}{2} . \frac{log 5}{log 5}$ - $\frac{2}{3} . \frac{log 2}{log 2}$

corta log 5 com log 5 e log 2 com log 2:

-4 + $\frac{1}{2} - \frac{2}{3}$
$\frac{-14}{3} + \frac{1}{2}$

calcula mmc entre 2 e 3:

$\frac{-28 + 3}{6} = \frac{-25}{6}$

espero ter ajudado.. beijos