Funkcja wykładnicza i logarytmy ! POMOCY NA JUTRO !   Oblicz:   Zad1 .  log₂₇3∛3=   Zad2. log₂8 + log½4 - log₉81 =   Zad3. log₆4 + log₆27 - log₆3 =   Zad3. log25 + 2log2 - log10⁴ =   Zad4. log₉(log₄(log₃)) =

Zad1 . log₂₇3∛3= log27 (3 * 3^(1/3)) = log27 3^(4/3) = 4/3 * log27 3 = 4/3 * log27 (27)^(1/3) = 4/3 * 1/3 * log27 27 = 44/9 * 1 = 4/9 Zad2. log₂8 + log½4 - log₉81 = log2 2^3 + log1/2 (1/2)^(-2) - log9 9^2 = 3 * log2 2 + (-2) * log1/2 1/2 - 2 * log9 9 = 3 * 1 - 2 * 1 - 2 * 1 = 3 - 2 - 2 = -1 Zad3. log₆4 + log₆27 - log₆3 = log6 (4 * 27 : 3) = log6 36 = log6 6^2 = 2 * log6 6 = 2 * 1 = 2 Zad3. log25 + 2log2 - log10⁴ = log 25 + log 2^2 - log 10^4 = log (25 * 4 : 10000) = log (100 : 10000 = log 1/100 = log 10^(-2) = -2 * log 10 = -2 * 1 = -2 Zad4. log₉(log₄(log₃ 9)) = log9 (log4 (log3 3^2)) = log9 (log4 (2 * log3 3)) =  log9 (log4 (2 * 1))  = log9 (log4 2 ) = log9 (log4 4^(1/2)) = log9 (1/2 * log4 4) = log 9 (1/2)