3^(log2 (5))-5^(log2(3))

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3^(log2(5))-5^(log2(3))3^(log2(5))-5^(log2(3))3^(log2(5))-5^(log2(3))令3^(log2(5))=m,5^(log2(3))=n,其中

3^(log2 (5))-5^(log2(3))
3^(log2 (5))-5^(log2(3))

3^(log2 (5))-5^(log2(3))
令3^(log2 (5))=m,5^(log2(3))=n,其中m>0,n>0
则log3 (m)=log2 (5),log5 (n)=log2 (3)
即lg m/lg 3=lg 5/lg 2,lg n/lg 5=lg 3/lg 2 (注:换底公式)
有lg m=(lg 5)*(lg 3)/lg 2,lg n=(lg 5)*(lg 3)/lg 2
所以lg m=lg n
即m=n
所以:
3^(log2 (5))-5^(log2(3))
=m-n
=0