Question

Aceste exerciții.Vă mulțumesc anticipat !​

Answer 1

Răspuns:

Explicație pas cu pas:

Cred la e) este eroare de tipar...

Answer 2

Explicație pas cu pas:

a)

$10 = log_{2}({2}^{10}) = log_{2}(1048) < log_{2}(2012) < log_{2}(2048) = log_{2}({2}^{11}) = 11$

$\implies \bf \Big[log_{2}(2012)\Big] = 10$

b)

$3 = lg({10}^{3}) = lg(1000) < lg(2012) < lg(10000) = lg({10}^{4}) = 4$

$\implies \bf \Big[lg(2012)\Big] = 3$

c)

$4 = log_{3}({3}^{4}) = log_{3}(81) < log_{3}(100) < log_{3}(243) = log_{3}({3}^{5}) = 5$

$\implies \bf \Big[log_{3}(100)\Big] = 4$

d)

$log_{ \frac{1}{2} }(9) = - log_{2}(9)$

$3 = log_{2}( {2}^{3} ) = log_{2}(8) < log_{2}(9) < log_{2}(16) = log_{2}({2}^{4}) = 4 \\ - 4 < - log_{2}(9) < - 3 \implies - 4 < log_{ \frac{1}{2} }(9) < - 3$

$\implies \bf \Big[log_{ \frac{1}{2} }(9)\Big] = - 4$

e)

$log_{0.1}(11) = log_{ \frac{1}{10} }(11) = - log_{10}(11)$

$1 = log_{10}(10) < log_{10}(11) < log_{10}(100) = log_{10}( {10}^{2} ) = 2 \\ - 2 < - log_{10}(11) < - 1 \implies - 2 < - log_{0.1}(11) < - 1$

$\implies \bf \Big[log_{0.1}(9)\Big] = - 2$

f)

$5 = log_{3}({3}^{5}) = log_{3}(243) < log_{3}(321) < log_{3}(729) = log_{3}({3}^{6}) = 6$

$\implies \bf \Big[log_{3}(321)\Big] = 5$