已知5^m=a,5n=b,求5^2m-n 5^2m-3n已知5^m=a,5n=b,求5^2m-n 5^2m-3n

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已知5^m=a,5n=b,求5^2m-n 5^2m-3n已知5^m=a,5n=b,求5^2m-n 5^2m-3n

已知5^m=a,5n=b,求5^2m-n 5^2m-3n已知5^m=a,5n=b,求5^2m-n 5^2m-3n
已知5^m=a,5n=b,求5^2m-n 5^2m-3n
已知5^m=a,5n=b,求5^2m-n 5^2m-3n

已知5^m=a,5n=b,求5^2m-n 5^2m-3n已知5^m=a,5n=b,求5^2m-n 5^2m-3n
5^(2m-n)=5^2m/5^n=a^2/b
5^2m-3n=5^2m/5^3n=a^2/b^3

5^m=a,5^n=b
5^(2m)=a²,
5^(3n)=b³
5^(2m-n)
=5^(2m)÷5^n
=a²÷b
=a²/b
5^(2m-3n)
=5^(2m)÷5^(3n)
=a²÷b³
=a²/b³
5^(2m-n)*5^(2m-3n)
=a²/b*a²/b³
=a⁴/b³

因为5^m=a,5n=b
所以m=log5*a,n=b/5
所以5^2m-n =5^2(log5*a)-n=a-b/5
5^2m-3n=5^2(log5*a)-3n=a-3b/5