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Popular >

simplify ln((s^2)/((s-9)^2))

Solution

simplify

ln (\frac{s ^{2}}{( s - 9 ) ^{2}})

Solution

2 ln (s) - 2 ln (s - 9)

Solution steps

ln (\frac{s ^{2}}{( s - 9 ) ^{2}})

Apply log rule:

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

ln (\frac{s ^{2}}{( s - 9 ) ^{2}}) = ln (s^{2}) - ln ((s - 9)^{2})

= ln (s^{2}) - ln ((s - 9)^{2})

Apply log rule:

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

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

= 2 ln (s) - ln ((s - 9)^{2})

Apply log rule:

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

ln ((s - 9)^{2}) = 2 ln (s - 9)

= 2 ln (s) - 2 ln (s - 9)

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Frequently Asked Questions (FAQ)

What is ln((s^2)/((s-9)^2)) ?
The solution to ln((s^2)/((s-9)^2)) is 2ln(s)-2ln(s-9)