Oblicz.
Korzystam z własności log
log a + log b = log(a*b)
log a - log b = log(a:b)
log a(do potegi 2) = 2log a
oraz korzystam z def. log
log 1000 = 3 , bo 10(podstawa log) do potęgi 3 = 1000
a) log 8+log 125 = log (8*125) = log 1000 =3
b) log₇ 19 - log₇ ¹⁹/₄₉ = log₇ 19 - ( log₇ 19- log₇ 49 ) = log₇ 19 - log₇ 19 + + log₇ 49 = 0 + 2 = 2
bo 7( podstawa log) do potegi 2 = 49
c) log 6-log 2-log 3 = log(2*3) - log 2 - log3 = log2 + log3- log 2 - log 3 = 0
d) log ⁷/₄-log 14-log125= log 7 - log4 - (log7*2) - log(5 do potęgi3) =
= log 7 - log 4 - (log7 + log 2) - 3 log 5=
= log 7 - log 4 - log7 - log 2 - 3 log 5=
= -2log2 - log 2 -3log 5 = -3log 2 -3 log 5 =
= -3( log2 + log5)
= -3( log 2*5)=
= -3*log 10=
= -3*1 = -3 , bo 10(podstawa log)do potęgi 1 = 10( liczba logarytmowana)
Wiadomo, że logx=¹/₃ oblicz:
a) log x⁶ = 6 log x = 6*(¹/₃) = 2
b) log ¹/x³= log 1 - log x³ = 0 - 3 logx = 0 -3*(¹/₃)= -1
c) log pierwiastek z x =( 1/2)*log x = (1/2)*(¹/₃) = 1/6
d)log ¹/pierwiastek z x do potęgi 3 = log 1 - (3/2)*logx= 0 - (3/2)*(¹/₃) = - 1/2
log 1 = 0, bo 10(podstawa log) do potegi 0 = 1( liczba logarytmowana)
