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secondary 3 | A Maths
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Tarah toh
Tarah Toh

secondary 3 chevron_right A Maths chevron_right Singapore

Help pleaseeeee

Date Posted: 4 years ago
Views: 426
Eric Nicholas K
Eric Nicholas K
4 years ago
Hi Tarah! I will do up the answers at 1 am if no one has already solved them by then.
snell
Snell
4 years ago
(a)(i)
log₅(x²-5x+20) = 1/log₂5 + 1/log₇5
=> log₅(x²-5x+20) = log2/log5 + log7/log5

=> log₅(x²-5x+20) = log₅2 + log₅7

=> log₅(x²-5x+20) = log₅14

=> x²-5x+20 = 14

=> x²-5x+6 = 0

=> (x-2)(x-3) = 0

=> x = 2 or 3



(a)(ii)
lg y² = (lg y)²
=> 2lg y = (lg y)²
=> (lg y)² - 2lg y = 0
=> lg y(lg y-2) = 0
=> lg y = 0 or lg y - 2 = 0
=> y = 1 or lg y = 2
=> y = 1 or y = 100


(b)
8e⁴ˣ - 15e²ˣ - 2 = 0
=> 8(e²ˣ)² - 15e²ˣ - 2 = 0
=> (8e²ˣ + 1)(e²ˣ - 2) = 0
=> e²ˣ = -1/8 (n.a.) or e²ˣ = 2
=> e²ˣ = 2
=> 2x = ln 2
=> x = (ln 2)/2 = 0.347


...

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Eric Nicholas K
Eric Nicholas K's answer
5997 answers (Tutor Details)
1st
Hi Tarah! Here are my workings for these questions. Let me know if you need more explanation on these.
Tarah toh
Tarah Toh
4 years ago
Clear steps
Eric Nicholas K
Eric Nicholas K
4 years ago
Ok, will write them up later or tmr when I am free
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Eric Nicholas K
Eric Nicholas K's answer
5997 answers (Tutor Details)
Before I proceed, here are certain laws of logarithms which you will need to know.
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Eric Nicholas K
Eric Nicholas K's answer
5997 answers (Tutor Details)
Here are my insights into how to solve Q1 a(i). In red are my explanations; in blue are the workings to include when you write up your answers.
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Eric Nicholas K
Eric Nicholas K's answer
5997 answers (Tutor Details)
Hi Tarah! Here are my explanations for Q1 a(ii).
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Eric Nicholas K
Eric Nicholas K's answer
5997 answers (Tutor Details)
And finally, this is for Q1 b.

I hope my explanations and workings help! Let me know if you still need more explanation for my workings and I will explain them again!