y=2^x sinx rewriting, |y|=2^x |sinx|
my questions, before taking the natural log for both sides and rearrange why do we need to rewrite using absolute value? why this particular question need to have absolute value?
2026-03-31 17:19:21.1774977561
usage of absolute value within natural log in solution of differential equation
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If you want to avoid complex numbers, the logarithm is only defined on $(0,\infty)$. So if $y$ happens to be negative, you can't take its logarithm. But $|y| \ge 0$ (there is still the possibility of $0$, but maybe that's not important in this example).