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The equation `(log)_(x^2) 16`+ `(log)_(2x)64=3 h a s`one irrationalsolution (b) no prime solutiontwo real solutions (d) no integral solutionA. one irrational solutionB. no prime solutionC. two real solutionsD. no integral solution |
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Answer» `L.H.S. =(1)/(log_(2^(4))x^(2))+(1)/(log_(2^(6))2x)=3implies(1)/(1//2log_(2)x)+(1)/(1//6(1+log_(2)x))=3"let"log_(2)x=y` `implies2/y+(6)/(1+y)=3implies2(1+y)+6y=3y(1+y)implies(y-2)(3y+1)=0impliesy=2ory=-1//3` `log_(2)x=2impliesx=4andlog_(2)x=(-1)/(3)impliesx=2^(-1//3)"]"` |
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