17~21算式+最佳解謝謝?

17)
原式 = (log4⁻¹ / log3) (log5⁻¹ / log4) (log6⁻¹ / log5) (log7⁻¹ / log6) (log8⁻¹ / log7) (log9⁻¹ / log8)
= (log4⁻¹ / log4) (log5⁻¹ / log5) (log6⁻¹ / log6) (log7⁻¹ / log7) (log8⁻¹ / log8) (log9⁻¹ / log3)
= (log4⁻¹ / log4) (log5⁻¹ / log5) (log6⁻¹ / log6) (log7⁻¹ / log7) (log8⁻¹ / log8) (log3⁻² / log3)
= (-1) (-1) (-1) (-1) (-1) (-2) = 2.

18)
原式 = (log3 / log2) (log64 / log7) (log5 / log3) (log49 / log5)
= (log64 / log2) (log49 / log7) = (6log2 / log2) (2log7 / log7) = 12.

19)
由條件知 x = a² = b³ = c⁴= d^5 , 則 abcd = x^(1/2 + 1/3 + 1/4 + 1/5)
故原式為 1 / (1/2 + 1/3 + 1/4 + 1/5) = 60/77.

20)
條件化為 a⁴= c^6 = e^15 , 原式約簡為 log e / log a = log c^(6/15) / log c^(6/4) = 6/15 / (6/4) = 4/15.

21)
a = 1 / (1 - log5 / log3) = log3 / (log3 - log5) = log3 / log(3/5)
;
3 = x^( log3 / log(3/5) )
x = 3/5.