Suppose that 4^(x_1) = 5, 5^(x_2) = 6, 6^(x_3) = 7,...., 126^(x_123) = 127, 127^(x_124) = 128. What is the value of the product x_1x_2...x_124?

1 Answer
Binayaka C.
Nov 27, 2016

3 1/2

Explanation:

4^(x_1)=5 . Taking log of both sides we get x_1log4=log5 or x_1=log5/log4.
5^(x_2)=6 . Taking log of both sides we get x_2 log5=log6 or x_2 =log6/log5.
6^(x_3)=7 . Taking log of both sides we get x_1log6=log7 or x_3=log7/log6.
..................
126^(x_123)=127 . Taking log of both sides we get x_123 log126=log127 or x_123=log127/log126.
127^(x_124)=128 . Taking log of both sides we get x_124 log127=log128 or x_124=log128/log127.
x_1*x_2*....*x124 = (cancellog5/log4) (cancellog6/cancellog5)(cancellog7/cancellog6)...log(cancel127/cancellog126)(log128/cancellog127) = log128/log4=log2^7/log2^2=(7cancellog2)/(2cancellog2)=7/2=3 1/2[Ans]

Related questions
See all questions in Systems Using Substitution
Impact of this question
3446 views around the world
You can reuse this answer
Creative Commons License