Question

Wiedząc że

log7 4=a i log7 3=b oblicz log7 36

log4 3=a i log4 5=b oblicz log4 1,8

log5 4=a i log5 27=b oblicz log5 6

log3 2=a i log3 7=b oblicz log3 14

Answer 1

A)
log₇ 4=a i log₇ 3=b oblicz log₇ 36
log₇ 36=log₇ (4*3*3)=log₇ 4+ log₇ 3+ log₇ 3=a+b+b=a+2b

b)
log₄ 3=a i log₄ 5=b oblicz log₄ 1,8
log₄ 1,8=log₄ (3*3:5)=log₄ 3+ log₄ 3- log₄ 5=a+a-b=2a-b

c)
log₅ 4=a i log₅ 27=b oblicz log₅ 6
a=log₅ 4=log₅ 2²=2log₅ 2
log₅ 2=½*a
b=log₅ 27=log₅ 3³=3log₅ 3
log₅ 3=⅓*b
log₅ 6=log₅ (2*3)=log₅ 2 +log₅ 3=½*a + ⅓*b

d)
log₃ 2=a i log₃ 7=b oblicz log₃ 14
log₃ 14=log₃ (2*7)=log₃ 2 +log₃ 7=a+b

Answer 2

A)log₇ 4=a i log₇ 3=b oblicz log₇ 36

log₇ 36=log₇ (4*3*3)=
=log₇ 4+ log₇ 3+ log₇ 3=
=a+b+b=
=a+2b

b)log₄ 3=a i log₄ 5=b oblicz log₄ 1,8

log₄ 1,8=log₄ (9/5)=log₄ (3*3:5)=
=log₄ 3+ log₄ 3- log₄ 5
=a+a-b=
=2a-b

c)log₅ 4=a i log₅ 27=b oblicz log₅ 6
log₅ 6=log₅ (2*3)
a=log₅ 4=log₅ 2²
a=2log₅ 2
½*a=log₅ 2
b=log₅ 27=log₅ 3³
b=3log₅ 3
⅓*b=log₅ 3
log₅ 6=log₅ (2*3)=log₅ 2 +log₅ 3=½*a + ⅓*b

d)log₃ 2=a i log₃ 7=b oblicz log₃ 14
log₃ 14=log₃ (2*7)=
=log₃ 2 +log₃ 7=
=a+b