Ask Singapore Homework?
Upload a photo of a Singapore homework and someone will email you the solution for free.
Question
secondary 3 | A Maths
2 Answers Below
Anyone can contribute an answer, even non-tutors.
Pls help !
Date Posted: 3 years ago
Views: 341
Given : log₆2 = a, log₅3 = b
log₅2
= log₅(6/3)
= log₅6 - log₅3
= log₅2/log₆2 - b
(Using the property logₐb = logₐc / logb c = log꜀b / log꜀a)
= log₅2 /a - b
Notice we have log₅2 on both sides.
Multiply both sides by a,
a log₅2 = log₅2 - ab
Bring over ab to the left and a log₅2 to the right,
log₅2 - a log₅2 = ab
(1 - a)log₅2 = ab
log₅2 = ab / (1 - a)
log₅2
= log₅(6/3)
= log₅6 - log₅3
= log₅2/log₆2 - b
(Using the property logₐb = logₐc / logb c = log꜀b / log꜀a)
= log₅2 /a - b
Notice we have log₅2 on both sides.
Multiply both sides by a,
a log₅2 = log₅2 - ab
Bring over ab to the left and a log₅2 to the right,
log₅2 - a log₅2 = ab
(1 - a)log₅2 = ab
log₅2 = ab / (1 - a)
Alternative working :
log₆2 = a ①
log₅3 = b ②
From ①,
1 / log₂6 = a
1/a = log₂6
1/a = log₂(3 × 2)
1/a = log₂3 + log₂2
1/a = log₂3 + 1
1/a - 1 = log₂3
(1 - a)/a = log₅3 / log₅2
(1 - a)/a = b / log₅2 (from ②)
(1 - a)/ab = 1 / log₅2
Flip both fractions,
ab/(1 - a) = log₅2 / 1 = log₅2
log₆2 = a ①
log₅3 = b ②
From ①,
1 / log₂6 = a
1/a = log₂6
1/a = log₂(3 × 2)
1/a = log₂3 + log₂2
1/a = log₂3 + 1
1/a - 1 = log₂3
(1 - a)/a = log₅3 / log₅2
(1 - a)/a = b / log₅2 (from ②)
(1 - a)/ab = 1 / log₅2
Flip both fractions,
ab/(1 - a) = log₅2 / 1 = log₅2
2nd alternative :
log₆2 = a
log₅2 / log₅6 = a
log₅2 / (log₅3 + log₅2) = a
log₅2 / (b + log₅2) = a
log₅2 = ab + alog₅2
ab = log₅2 (1 - a)
log₅2 = ab/(1 - a)
log₆2 = a
log₅2 / log₅6 = a
log₅2 / (log₅3 + log₅2) = a
log₅2 / (b + log₅2) = a
log₅2 = ab + alog₅2
ab = log₅2 (1 - a)
log₅2 = ab/(1 - a)
See 2 Answers
The answer is ab/1-b, different from the solution given
It's actually ab/(1 - a). See the main comments section for my working.
Answers in main comments
360 Tutoring Program