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

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Assumption needed is p is positive except for 1.

Date Posted:
2 months ago

Thankuu!!

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

This works because p^ and base p in the log are inverses of one another.