ln (x^r) =
r ln x
r ln(x)
The above expression represents the logarithm of x raised to the power of r. It can be simplified using the rules of logarithms, specifically the rule that states that the logarithm of a number raised to a power is equal to the product of that power and the logarithm of the number. Therefore, ln(x^r) can be rewritten as r ln(x). This means that if we know the value of x and r, we can use this expression to find the value of the logarithm. For example, if x=2 and r=3, ln(2^3) = 3 ln(2) = 3 x 0.69314718 = 2.07944154.
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