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## Homework Statement

We are required to find the no. of ordered pairs ##(x,y)## satisfying the equation

##13+12[tan^{-1}x]=24[ln x]+8[e^x]+6[cos^{-1}y]##. (##[.]## is the greatest integer function, e.g. ##[2.3]=2##, ##[5.6]=5##, ##[-2.5]=-3## etc)

## Homework Equations

## The Attempt at a Solution

The answer happens to be zero. I tried to arrange the terms so that I can show that the ranges on either side of the equation don't overlap, but the logarithmic and exponential terms always make the range the set of real numbers, so that doesn't work. Also, the constraint on the domain is that ##x## must be positive because of the logarithm term. I then tried to study two cases ##x>1## and then ##x## between zero and one. But I haven't made any progress. Any help would be appreciated; thanks in advance!