What is ln((r^2)/(r^1)) ?

The solution to ln((r^2)/(r^1)) is ln(r)

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simplify ln((r^2)/(r^1))

simplify

ln (\frac{r ^{2}}{r ^{1}})

ln (r)

Solution steps

ln (\frac{r ^{2}}{r ^{1}})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{r ^{2}}{r ^{1}}) = ln (r^{2}) - ln (r^{1})

= ln (r^{2}) - ln (r^{1})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (r^{2}) = 2 ln (r)

= 2 ln (r) - ln (r^{1})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (r^{1}) = 1 \cdot ln (r)

= 2 ln (r) - 1 \cdot ln (r)

Add similar elements:

2 ln (r) - 1 \cdot ln (r) = ln (r)

= ln (r)

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