What is simplify-ln((k^2)/(k^1)) ?

The solution to simplify-ln((k^2)/(k^1)) is -ln(k)

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simplify-ln((k^2)/(k^1))

simplify

- ln (\frac{k ^{2}}{k ^{1}})

- ln (k)

Solution steps

- ln (\frac{k ^{2}}{k ^{1}})

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Add similar elements:

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

= - ln (k)

- lo g_{10} (5.8 \cdot 1 0^{- 8})

ln (8 \cdot e^{- 8 x})

800 ln (20) - 400 - 800 ln (10)

\frac{1}{3} ln (\frac{26}{7})

ln (\frac{49}{4})

What is simplify-ln((k^2)/(k^1)) ?
The solution to simplify-ln((k^2)/(k^1)) is -ln(k)