4 ^(x_1)= 5、5 ^(x_2)= 6、6 ^(x_3)= 7、...、126 ^(x_123)= 127、127 ^(x_124)= 128とします。製品の値x_1x_2 ... x_124?

4 ^(x_1)= 5、5 ^(x_2)= 6、6 ^(x_3)= 7、...、126 ^(x_123)= 127、127 ^(x_124)= 128とします。製品の値x_1x_2 ... x_124?
Anonim

回答:

#3 1/2#

説明:

#4 ^(x_1)= 5#。両側のログを取る #x_1log4 = log5またはx_1 = log5 / log4#.

#5 ^(x_2)= 6#。両側のログを取る #x_2 log5 = log6またはx_2 = log6 / log5#.

#6 ^(x_3)= 7#。両側のログを取る #x_1log6 = log7またはx_3 = log7 / log6#.

#………………#

#126 ^(x_123)= 127#。両側のログを取る #x_123 log126 = log127またはx_123 = log127 / log126#.

#127 ^(x_124)= 128#。両側のログを取る #x_124 log127 = log128または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