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:
$$
f(x) =8^{\log_{8}({x-3})}
$$
After defining the range of the arguments the function may be reduced to $f(x) = x-3$ where $x \gt 3$, which eventually appears to be a linear function.
It's clear that the range of $x$ is restricted to $x>3$ in $\mathbb R$ since $\log(x)$ is not defined for $x \le 0$. But wolfram alpha expands the line below the X-axis and shows that the function exists for $x \le 3$
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. $$\log_8(-|x|)=\log_8(|x|e^{i\pi})=\log_8|x|+\log_8e^{i\pi}=\log_8|x|+i\pi\frac{1}{\ln 8}$$
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