如果2^x=5^y=10^z,试以x及y表示z.请付过程?
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如果2^x=5^y=10^z,试以x及y表示z.请付过程?
2^x = 10^z
lg 2^x = lg 10^z
xlg2 = zlg10 z = x lg2
5^y = 10^z
lg5^y = lg10^z
y lg5 = z lg10 z= y lg5
再问: 为什么z=xy/(x+y) ???怎么计算出来?
再答: 上述式子: z = x lg2 z/x = 1g2 (1) z = y lg5 z/y = 1g5 (2) (1)(2)相加: z/x + z/y = 1g2 + 1g5 z/x + z/y = 1g10 z/x + z/y = 1 z = 1/(1/x + 1/y) = 1/[(x+y)/xy] =xy / (x+y)
lg 2^x = lg 10^z
xlg2 = zlg10 z = x lg2
5^y = 10^z
lg5^y = lg10^z
y lg5 = z lg10 z= y lg5
再问: 为什么z=xy/(x+y) ???怎么计算出来?
再答: 上述式子: z = x lg2 z/x = 1g2 (1) z = y lg5 z/y = 1g5 (2) (1)(2)相加: z/x + z/y = 1g2 + 1g5 z/x + z/y = 1g10 z/x + z/y = 1 z = 1/(1/x + 1/y) = 1/[(x+y)/xy] =xy / (x+y)
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