高一数学计算题
3个回答
展开全部
7^(lg20)x(0.5)^(lg0.7)
=(10^lg7)^lg20 *(10^lg0.5)^lg0.7
=10^(lg7*lg20+lg0.5*lg0.7)
=10^[lg7*(1+lg2)+(lg5-1)*(lg7-1)]
=10^(lg7*lg2+lg7*lg5-lg5+1)
=10^(lg7-lg5+1)
=10^(lg7+lg2)
=10^lg14
=14
法二:
令7^(lg20)*(0.5)^(lg0.7)=t
lg^7^lg20+lg^0.5^lg0.7=lg^t
lg20(lg7)+lg0.7lgO.5=lg^t
[lg2*10]*lg7+(lg7-l)lg^0.5=lg^t
(lg2+1)lg7+(lg7-1)(-lg2)=lg^t
lg2*lg7+lg7-lg7*lg2+lg2=lg^t
lg7+lg2=lgt
lg(7*2)=lgt
所以t=14
=(10^lg7)^lg20 *(10^lg0.5)^lg0.7
=10^(lg7*lg20+lg0.5*lg0.7)
=10^[lg7*(1+lg2)+(lg5-1)*(lg7-1)]
=10^(lg7*lg2+lg7*lg5-lg5+1)
=10^(lg7-lg5+1)
=10^(lg7+lg2)
=10^lg14
=14
法二:
令7^(lg20)*(0.5)^(lg0.7)=t
lg^7^lg20+lg^0.5^lg0.7=lg^t
lg20(lg7)+lg0.7lgO.5=lg^t
[lg2*10]*lg7+(lg7-l)lg^0.5=lg^t
(lg2+1)lg7+(lg7-1)(-lg2)=lg^t
lg2*lg7+lg7-lg7*lg2+lg2=lg^t
lg7+lg2=lgt
lg(7*2)=lgt
所以t=14
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