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Popular >

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

Solution

simplify

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

Solution

ln (v)

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Add similar elements:

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

= ln (v)

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Frequently Asked Questions (FAQ)

What is ln((v^2)/(v^1)) ?
The solution to ln((v^2)/(v^1)) is ln(v)