1.Doprowadź potęgi do wspólnej postaci: a) (^3√9)^2 b) (1/3)^-5 2. Oblicz: 1. log2 8 +log1/2 4 +log9 81 2.log6 4 + log6 27-log6 3 3.log4(log3(log2 8)) 4.log3√3/81 5.log1/5 5√5 :)

a) ^3√9)^2 = (^3√(3)^2)^2 =((3)^(2/3))^2 =(3)^(2/3)*2 =3^(4/3) b) (1/3)^-5=3^(-1*-5)=3^5 1. log2 8 +log1/2 4 +log9 81= 3-2+2=3 log2 8=x log1/2 4=y log9 81=z 2^x=8 (1/2)^y=4 9^z=81 x=3 y=-2 z=2 2.log6 4 + log6 27-log6 3=log6 (4*27)-log6 3=log6 (4*27:3)= log6 36=2 log6 36=x 6^x=36 x=2 3. z pierwszego log2 8=x ---->x=3 log4(log3(log2 8))=log4(log3 3)=log4 1=0 log4 1=x 4^x=1 x=0 5.log1/5 5√5=log1/5 5^(3/2)=(3/2)*log1/5 5=(3/2)*(-1)=-3/2 log1/5 5=x 1/5^x=5 x=-1