Oblicz;
a) log(2 na dole)8
b) log(1/2 na dole)32
c) log(3 na dole)√27
d) log(1/5 na dole)1
d) log(2/3 na dole)[tex]\frac{3}{2}[/tex]
a) log(2 na dole)8
b) log(1/2 na dole)32
c) log(3 na dole)√27
d) log(1/5 na dole)1
d) log(2/3 na dole)[tex]\frac{3}{2}[/tex]
Odpowiedź:
a) [tex]log_2 8 = 3[/tex] bo 2³ = 8
b ) [tex]log_{1/2} 32 = - 5[/tex] bo [tex](\frac{1}{2} )^{-5} = 2^5 = 32[/tex]
c ) [tex]log_3 \sqrt{27} = log_3 27^{1/2} = \frac{1}{2} *log_3 27 = 0,5*3 = 1,5[/tex]
[tex]log_3 27 = 3[/tex] bo [tex]3^3 = 27[/tex]
d ) [tex]log_{1/5} 1 = 0[/tex] bo ( [tex]\frac{1}{5} )^0 = 1[/tex]
e ) [tex]log_{2/3} \frac{3}{2} = -1[/tex] bo ( [tex]\frac{2}{3} )^{-1} = \frac{3}{2}[/tex]
Szczegółowe wyjaśnienie:
[tex]log_a x = b[/tex] ⇔ [tex]a^b = x[/tex]
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