r ln(x)
This is because ln stands for the natural logarithm, which is the logarithm with base e. For any positive base b and exponent r, we can write:
b^r = e^(ln(b^r))
Using the rules of logarithms, we can simplify:
b^r = e^(r ln(b))
Taking the natural logarithm of both sides gives us:
ln(b^r) = r ln(b)
So, for ln(x^r), we can let b = x and get:
ln(x^r) = r ln(x)
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