Usando a definicão de logaritmo, calcule: a) log_(3)27 d) log_((1)/(2))32 g) log_(2)sqrt (8) b) log_(5)125 e) log_(10)0,01 h) log_(4)sqrt (32) c) log10000 F) log_(2)0,5 i) log_((1)/(4))16

Question

Pergunta

Answer 1

a)

$log_{3}27 = 3$ , pois

$3^3 = 27$ .

b)

$log_{5}125 = 3$ , pois

$5^3 = 125$ .

c)

$log10000 = 4$ , pois

$10^4 = 10000$ .

d)

$log_{\frac {1}{2}}32 = -5$ , pois

$(\frac {1}{2})^{-5} = 32$ .

e)

$log_{10}0,01 = -2$ , pois

$10^{-2} = 0,01$ .

f)

$log_{2}0,5 = -1$ , pois

$2^{-1} = 0,5$ .

g)

$log_{2}\sqrt {8} = \frac {3}{2}$ , pois

$2^{\frac {3}{2}} = \sqrt {8}$ .

h)

$log_{4}\sqrt {32} = \frac {5}{2}$ , pois

$4^{\frac {5}{2}} = \sqrt {32}$ .

i)

$log_{\frac {1}{4}}16 = -2$ , pois

$(\frac {1}{4})^{-2} = 16$ .