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標題:
Exponential Functions
發問:
1.If ^3√7^2m=16.find the values of the following without finding value of m (a)49^m (b) √7^3m 2. It is given that 10^a=100^b=1000^c,where a,b and c are non-zero constants.Find a:b:c 更新: why a:b:c=6:3:2,please explain.
最佳解答:
1. (7^(2m))^(1/3) = 16 7^(2m) = 16^3 (7^m)^2 = 4096 7^m = √(4096) 7^m = 64 a) 49^m = (7^2)^m = (7^m)^2 = 64^2 = 4096 b) √(7^(3m)) = √((7^m)^3) = √(64^3) = √(262144) = 512 2. 10^a = 100^b = 1000^c 10^a = (10^2)^b = (10^3)^c 10^a = 10^(2b) = 10^(3c) a = 2b = 3c So, a:b:c = 6:3:2 2011-11-19 17:23:54 補充： a = 2b b = a/2 a = 3c c = a/3 so a:b:c = a:a/2:a/3 = 1:1/2:1/3 multiply the equation by the LCM (which is 6), = 6:3:2
其他解答:
Exponential Functions
發問:
1.If ^3√7^2m=16.find the values of the following without finding value of m (a)49^m (b) √7^3m 2. It is given that 10^a=100^b=1000^c,where a,b and c are non-zero constants.Find a:b:c 更新: why a:b:c=6:3:2,please explain.
最佳解答:
1. (7^(2m))^(1/3) = 16 7^(2m) = 16^3 (7^m)^2 = 4096 7^m = √(4096) 7^m = 64 a) 49^m = (7^2)^m = (7^m)^2 = 64^2 = 4096 b) √(7^(3m)) = √((7^m)^3) = √(64^3) = √(262144) = 512 2. 10^a = 100^b = 1000^c 10^a = (10^2)^b = (10^3)^c 10^a = 10^(2b) = 10^(3c) a = 2b = 3c So, a:b:c = 6:3:2 2011-11-19 17:23:54 補充： a = 2b b = a/2 a = 3c c = a/3 so a:b:c = a:a/2:a/3 = 1:1/2:1/3 multiply the equation by the LCM (which is 6), = 6:3:2
其他解答:
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