求值 100^(1/2lg9-lg2)=

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求值 100^(1/2lg9-lg2)=
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求值 100^(1/2lg9-lg2)=
求值 100^(1/2lg9-lg2)=

求值 100^(1/2lg9-lg2)=
原式=
10^2(1/2lg9-lg2)
=10^(lg9-lg4)
=10^lg(9/4)
设lg(9/4)=t
则10^t=9/4
所以10^lg(9/4)=9/4

100^(1/2lg9-lg2)
=100^{1/2(lg9-2lg2)}
=100^{1/2(lg9-lg4)}
=100^1/2(lg9/4)
=100^lg3/2
=100^log100<在下>3/2^2<在上>
=9/4

100^(1/2lg9-lg2)
=100^{[lg(9)^1/2]-lg2}
=100^{lg3-lg2}
=100^lg(3/2)
=10^2lg(3/2)
=10^lg(9/4)
=9/4