1. Oblicza) b) c) d) 2.Oblicz a) b) c).... Question from @asia12162

asia12162 @asia12162

October 2018 1 36 Report

1. Oblicz

a) $log x_2_7 3\sqrt3$

b) $27^l^o^g _32$

c) $\sqrt27^l^o^g_3 2$

d) $3^1^-^l^o^g_3 2$

2.Oblicz $log_2 a$

a) $log_a 2=\frac{1}{2}$

b) $log _a 8=6$

c) $log_a 32=-5$

irenas

$log_{27}3\sqrt{3}=x\\27^x=3\sqrt{3}\\(3^3)^x=3^1\cdot3^{\frac{1}{2}}\\3^{3x}=3^{\frac{3}{2}}\\3x=\frac{3}{2}\\x=\frac{1}{2}$

$27^{log_32}=(3^3)^{log_32}=3^{3log_32}=3^{log_32^3}=2^3=8$

$(\sqrt{27})^{log_32}=[(3^3})^{\frac{1}{2}}]^{log_32}=3^{\frac{3}{2}log_32}=3^{log_32^{\frac{3}{2}}}=2^{\frac{3}{2}}=2\sqrt{2}$

$3^{1-log_32}=\frac{3}{3^{log_32}}=\frac{3}{2}$

$a>0\ \ i\ \ a\neq1$

$log_a2=\frac{1}{2}\\a^{\frac{1}{2}}=2\\a=2^2=4$

$log_a8=6\\a^6=8\\(a^2)^3=2^3\\a^2=2\\a=\sqrt{2}$

$log_a32=-5\\a^{-5}=32\\a^{-5}=2^5\\a^{-5}=(\frac{1}{2})^{-5}\\a=\frac{1}{2}$

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