Вычислите значение функции f (x) = log3 (tg п/3)

Question

Математика

Мирра

2 июля, 13:15

Вычислите значение функции f (x) = log3 (tg п/3)

+3

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Ульян · Answer 1

1) Log3 4 - log3 16 + log3 4/9 = Log3 4 / 16 + log3 4/9=Log3 ((4/16) * (4/9)) = Log3 1/9=

Log3 (3) ^-2 = - 2

2) 2 log7 27 - log7 81-2 log7 21=log7 27^2 / 81-2 log7 21 = log7 729 / 81 - log7 21 ^2 = log7 9 - log7 21 ^2 = log7 (9 / 441) = log7 (1 / 49) = log7 (7^-2) = - 2

3) 2 log2 8 + log2 15/4 - log2 15=log2 (8^2 * (15/4)) - log2 15 = log2 ((64*15) / 4) - log2 15 =

log2 (16*15) - log2 15 = log2 ((16*15) / 15) = log2 (16) = log2 (2^4) = 4

4) log3 7 * log4 81 * log7 2 = log4 81 * log7 2*1 / log7 3 = log4 3^4 * (log7 2 / log7 3) =

4 * log4 3 * log3 2=4 * log3 2 * (1 / log3 4) = 4 * log3 2 * (1 / log3 2^2) = 4 * log3 2 * (1 / 2 log3 2) = (4 * log3 2) / (2 log3 2) = 4/2=2

5) Lg3 (log3 25+log3 2-log3 5) = Lg3 (log3 (25 * 2) - log3 5) = Lg3 (log3 50 / 5) = Lg3*log3 10 = log10 3 * log3 10 = log10 3 / log10 3=1