Question

log 1/4 2raiz de 2
log 10 0,01 = X

Answer 1

Resolver os logaritmos:

$\sf{\log_{\frac{1}{4}} (2\sqrt{2})}$

$\sf{\log_{4^{-1}} (2 \times 2^{\frac{1}{2}})}$

$\sf{\log_{(2^2)^{-1}} (2^{1 + \frac{1}{2}})}$

$\sf{\log_{2^{-2}} (2^{\frac{3}{2}})}$

Usando $\sf{\log_{a^y} (a^x) = \dfrac{x}{y}}$ :

$= \sf{\dfrac{3}{\dfrac{2}{ - 2}}}$

$\sf{ = \dfrac{3}{2 \times ( - 2)}}$

$\blue{\boxed{\sf{= - \dfrac{3}{4}}}}$

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$\sf{\log_{10} (0,01) = x}$

$\sf{\log_{10} (\dfrac{1}{100}) = x}$

$\sf{\log_{10} (100^{-1}) = x}$

$\sf{\log_{10} ((10^2)^{-1}) = x}$

$\sf{\log_{10} (10^{2 \times (-1)}) = x}$

$\sf{\log_{10} (10^{-2}) = x}$

Usando $\sf{\log_{a} (a^x) = x}$ :

$\blue{\boxed{\sf{x = - 2}}}$