Eric Nicholas K's answer to kim Yeon Jae's Secondary 4 A Maths Singapore question.

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Eric Nicholas K
Eric Nicholas K's answer
3794 answers (Tutor Details)
1st
Assumption needed is p is positive except for 1.
kim Yeon Jae
Kim Yeon Jae
2 months ago
Thankuu!!
J
J
2 months ago
Shorter alternative :

2xp^(4logp(x)) = 486

xp^(logp(x⁴)) = 243

x(x⁴) = 243

x^5 = 3^5

x = 3

(Useful property to remember :
a^(loga(b)) = b

Similar : e^(ln b) = b
10^(lg b) = b

To see why it's so,

a^(loga(b)) = b

Take log a on both sides,
loga(b) = loga(b)

No need to assume p ≠ 1 . Because log base cannot be 1 or else it's undefined. Rather, it's deduced or inferred that p ≠ 1
Eric Nicholas K
Eric Nicholas K
2 months ago
This works because p^ and base p in the log are inverses of one another.