Question

4.1. Oblicz a) log2 z 27 + log2 z 2/9 + log2 z 2/3 b) log3 z 4 + log3 z 3/2 + log3 z 81/2 c) log5 z 7 + log5 z 6/14 + log5 z (8 1/3) d) log6 z 34 + log6 z 2/17 + log6 9 4.2. Oblicz a) log5 z 150 - log5 z 3 - log5 z 2 b) log4 z 3 - log 5 z 3 - log 5z 2 c) log 6 z 2 - log6 z 7/3 - log6 z 1/42 d) log4 z (1 i 3/13) - log4 z (3 i 1/2) - log4 z 1/91

Answer 1

4.1

 

a ) 

 

log2 27 + (log2 2 - log2 9) +( log2 2 - log2 3) = log2 54 - log2 18 - log2 3 = log2 54 - log2 54 = log2 2 = 1 

 

b) 

 

log3 4 + ( log3 3 - log3 2 ) + ( log3 81 - log3 2 ) = log3 6 + log3 40,5 = log3 243 = 5 

 

c ) 

 

log5 7 + ( log5 6 - log5 14 ) + ( log5 25 - log5 3 ) = log5 3 + log5 25/3 = log5 25 = 2 

 

d ) 

 

log6 34 + ( log6 2 - log6 17 ) + log6 9 = log6 68 - log6 17 + log6 9 = log6 4 + log6 9 = log6 36 = 6

 

4.2 

 

a) 

 

log5 150 - log5 3 - log5 2 = log5 50 - log5 2 = log5 25 = 2 

 

b) 

 

log4 3 - log 5 3 - log 5 2 = log5 3 / log5 4 - log5 3 - log5 2 

 

c)

 

log6 2 - ( log6 7 - log6 3 ) - ( log6 1 - log6 42 ) = ( log6 6 + log6 1/3 ) -  log6 7 - ( log6 6 + log6 1/2 )  - ( log6 6 + log 6 7)  = 1 + log6 1/3 - log 6 7 - 1 + log6 1/2 - 1 + log6 7 =  log6 1/3 - log6 7 + log6 1/2  - 3 

 

 

 

d)

 

( log4 z 16 - log4 13 ) - ( log4 7 - log4 2 ) - ( log4 1 - log4 91 ) = 1 - log4 13 - log4 7 - 1/2 - 0 - log4 91 = 3/2 - log4 13 - log4 7 - log4 91 = log4 1/49 - 3/2