已lg2=0.3010,lg3=0.4771.lg7=0.8451,求0.5是5的几次幂(对数)

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已lg2=0.3010,lg3=0.4771.lg7=0.8451,求0.5是5的几次幂(对数)
已lg2=0.3010,lg3=0.4771.lg7=0.8451,求0.5是5的几次幂(对数)

已lg2=0.3010,lg3=0.4771.lg7=0.8451,求0.5是5的几次幂(对数)
设0.5是5的n次幂.
5^n =0.5
两边同取对数,
lg (5^n) = lg 0.5
n*lg5 =lg (1/2) = -lg2
n *lg(10/2) = -lg2
n *(lg10-lg2) = -lg2
n = -lg2/(1-lg2) = -0.3010/(1-0.3010) = -0.4306
所以,0.5是5的 (-0.4306) 次幂

5^x=0.5 推出 x=lg(0.5)/lg5=-lg2/(1-lg2)数据自己代入