請教兩題有關指數和對數的問題

[changhunch]

拜託了

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#1
1-sin(2θ)=(sinθ)^2+(cosθ)^2-2sinθ*cosθ=(sinθ-cosθ)^2
cos(θ+Pi/4)=cosθ*cos(Pi/4) -sinθ*sin(Pi/4) =(1/2^0.5)*(cosθ-sinθ)

所求=Log(1/2 ,|sinθ-cosθ|) - Log(1/2 ,(1/2^0.5)*(cosθ-sinθ) )
=Log(1/2 ,cosθ-sinθ) - Log(1/2 ,(1/2^0.5)*(cosθ-sinθ) ) ( 因為0<θ<Pi/4 ,所以|sinθ-cosθ|=cosθ-sinθ)
=Log(1/2 ,2^0.5)
=(-1/2)*Log(2,2)
=(-1/2)*1
=-1/2

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#2
令3^x=4^y=6^z=k
則x=log(3,k) ,y=log(4,k) ,z=log(6,k)
4y=4*log(4,k)=(4/log(10,4))* log(10,k) =約 6.64* log(10,k)
5z=5*log(6,k)=(5/log(10,6))* log(10,k) =約 6.43* log(10,k)
3x=3*log(3,k)=(3/log(10,3))* log(10,k) =約 6.29* log(10,k)
所以4y>5z>3x

[changhunch]

謝謝，我懂了