Sunday, 4 November 2018

algebra precalculus - Why is wolfram plotting a wrong graph for f(x)=8log8(x3)?




I'm manually plotting various functions' graphs and use desmos and wolfram to validate whether I've analyzed the function in a correct way. But then I came to the following function and it seems that wolfram is showing a wrong result:



f(x)=8log8(x3)



After defining the range of the arguments the function may be reduced to f(x)=x3 where x>3, which eventually appears to be a linear function.



It's clear that the range of x is restricted to x>3 in R since log(x) is not defined for x0. But wolfram alpha expands the line below the X-axis and shows that the function exists for x3




Am I missing something or is that just wolfram reducing the function and plotting the graph for the result?


Answer



Because Wolfram can deal with complex numbers. log8(|x|)=log8(|x|eiπ)=log8|x|+log8eiπ=log8|x|+iπ1ln8


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