Proszę o pomoc! Wykaż, że x jest liczbą całkowitą, gdy =log59 + 2(log51-log53)
x = log 5 [ 9 ] + 2 ( log 5 [ 1 ] - log 5 [ 3 ] ) =
= log 5 [ 9] + 2 ( log 5 [ 1/3 ] = log 5 [ 9 ] + log 5 [ (1/3)^2] =
= log 5 [ 9] + log 5 [ 1/9] = log 5 [ 9 *(1/9) ] = log 5 [ 1 ] = 0 - czyli liczba całkowita.
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x = log 5 [ 9 ] + 2 ( log 5 [ 1 ] - log 5 [ 3 ] ) =
= log 5 [ 9] + 2 ( log 5 [ 1/3 ] = log 5 [ 9 ] + log 5 [ (1/3)^2] =
= log 5 [ 9] + log 5 [ 1/9] = log 5 [ 9 *(1/9) ] = log 5 [ 1 ] = 0 - czyli liczba całkowita.