Nilai dari a log 1/b x b log1/c^2 x c log 1/d^3 x d log 1/e^4 x e log 1/a^5 adalah.... A. 120 B. 1/120 C. 0 D. -1/120 E. -120 Tolong pakai cara ya...

a log (1/b) x b log (1/c^2) x c log (1/d^3) x d log (1/e^4) x e log (1/a^5) =
[ a log 1 - a log b ] × [ b log 1 - b log c² ] ×
[ c log 1 - c log d³ ] × [ d log 1 - d log e⁴ ] ×
[ e log 1 - e log a^5 ] =
[ 0 - a log b ] × [ 0 - b log c² ] ×
[ 0 - c log d³ ] × [ 0 - d log e⁴ ] ×
[ 0 - e log a^5 ] =
[ - a log b ] × [ - b log c² ] × [ - c log d³ ] ×
[ - d log e⁴ ] × [ - e log a^5 ] =
(-1)(-1)(-1)(-1)(-1) [ a log b ] × [ b log c² ] ×
[ c log d³ ] × [ d log e⁴ ] × [ e log a^5 ] =
(-1) [ a log b ] × [ 2 b log c ] × [ 3 c log d ] ×
[ 4 d log e ] × [ 5 e log a ] =
(-1)(2)(3)(4)(5) [ a log b] × [ b log c ] ×
[ c log d ] × [ d log e ] × [ e log a ] =
(-120) ( a log a ) =
(-120) (1) = - 120

Jadi, hasilnya - 120 (E)