Question

Determine o valor do logaritmo abaixo: 
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Answer 1

Explicação passo-a-passo:

g)

$\sf log_{2}~x=5$

$\sf x=2^5$

$\sf x=2\cdot2\cdot2\cdot2\cdot2$

$\sf \red{x=32}$

c)

$\sf log_{4}~\sqrt{32}=x$

$\sf 4^x=\sqrt{32}$

$\sf (2^2)^x=\sqrt{2^5}$

$\sf 2^{2x}=2^{\frac{5}{2}}$

Igualando os expoentes:

$\sf 2x=\dfrac{5}{2}$

$\sf 2\cdot2x=5$

$\sf 4x=5$

$\sf x=\dfrac{5}{4}$

$\sf \red{x=1,25}$

a outra:

$\sf log_{2}~2^{-3}=\red{-3}$, pois $\sf log_{a}~a^n=n$