Exponentialgleichung und Logarithmen

Question

wie berechne ich die folgenden Aufgaben?

a) log₃(9^4)

b)log₅( 125^-1)

c) log₃(\( \sqrt{27} \)^-1)

      

Answer 1

a) 9^4 = 3^8 → 3^x = 3^8  → x=8

b) 125^(-1) = 5^(-3) → x= -3

c) √27 ^(-1) = (3^(3/2))^)-1 = 3^(-3/2) → x= -3/2

Answer 2

a) 4 * log₃(9) = 4 * log₃(3^2) = 4 * 2 * log₃(3) = 4 * 2 * 1 = 8

b) - log5(125) = - log5(5^3) = -3 * log5(5) = -3 * 1 = -3

c) log₃( (27^1/2)^-1 ) = log₃(27^-1/2) = -0.5 * log₃(27) = ...

Answer 3

a) log₃(9⁴) =log₃(3⁸) =8

b)log₅( 125^-1)=log₅(5^-3)= -3

c) log₃((√27)^-1) =log₃(3^-3/2)=-3/2