Monday, 16 December 2013

trigonometry - Find domain of function logleft(cosleft(logxright)right)




Find domain of function f(x)=log(cos(logx))




At the beginning x>0
but I have no idea how to handle logarithm
cos(logx)>0logx>arccos0=π2logx>log10π2x>10π2
I think I'm doing something wrong



Answer



We need




  • x>0


  • cos(logx)>0




0logx<π2π2+2nπ<logx<π2+2nπ


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