Question

Wiedząc, że:

a) log₃ 2 = a, oblicz log₂ 13,5

b) log₂ 5 = b, oblicz log₂ 400

c) log₅ 2 = a i log₅ 7 = b, oblicz log₁₂₅ 28

d) log₆ 2 = a i log₆ 5 = b, oblicz log₃₆ 0,8

Answer 1

a) log₂ 13,5= log₂27/2=log_3(27/2)/log_3(2)=(log_3(27)-log_3(2))/a=3-a / a

b) log₂ 400=log₂ (25*16)=log₂ 25+log₂ 16=log₂ 5^2+4=2log₂5+4=2b+4

c) oblicz log₁₂₅ 28=log₅ 28/log₅ 125=log₅ (4*7)/3=log₅ 4+log₅ 7 /3=log₅ 2^2+b /3=

2log₅ 2+b /3=(2a+b)/3

d) log₃₆ 0,8=log₆ 0,8/log₆ 36=log₆ (4/5)/2=log₆ 4-log₆ 5 / 2= (2a-b)/2

Answer 2

 

wzory logarytmow w zalaczniku.