What is ln(((s^2+c^2)(s+a))/((s+b)(s^2-c^2))) ?

The solution to ln(((s^2+c^2)(s+a))/((s+b)(s^2-c^2))) is ln(s^2+c^2)+ln(s+a)-ln(s+b)-ln(s^2-c^2)

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simplify ln(((s^2+c^2)(s+a))/((s+b)(s^2-c^2)))

simplify

ln (\frac{( s ^{2} + c ^{2} ) ( s + a )}{( s + b ) ( s ^{2} - c ^{2} )})

ln (s^{2} + c^{2}) + ln (s + a) - ln (s + b) - ln (s^{2} - c^{2})

Solution steps

ln (\frac{( s ^{2} + c ^{2} ) ( s + a )}{( s + b ) ( s ^{2} - c ^{2} )})

Apply log rule:

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

ln (\frac{( s ^{2} + c ^{2} ) ( s + a )}{( s + b ) ( s ^{2} - c ^{2} )}) = ln ((s^{2} + c^{2}) (s + a)) - ln ((s + b) (s^{2} - c^{2}))

= ln ((s^{2} + c^{2}) (s + a)) - ln ((s + b) (s^{2} - c^{2}))

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln ((s^{2} + c^{2}) (s + a)) = ln (s^{2} + c^{2}) + ln (s + a), ln ((s + b) (s^{2} - c^{2})) = ln (s + b) + ln (s^{2} - c^{2})

= ln (s^{2} + c^{2}) + ln (s + a) - (ln (s + b) + ln (s^{2} - c^{2}))

- (ln (s + b) + ln (s^{2} - c^{2})) : - ln (s + b) - ln (s^{2} - c^{2})

= ln (s^{2} + c^{2}) + ln (s + a) - ln (s + b) - ln (s^{2} - c^{2})

3.34678 + lo g_{10} (\frac{0.01}{0.2})

lo g_{6} (\frac{f}{36})

- lo g_{10} (2.1 \cdot 1 0^{- 3})

lo g_{3} (7) - lo g_{3} (x)

lo g_{10} (\frac{x ^{2} + y ^{2}}{10000})

What is ln(((s^2+c^2)(s+a))/((s+b)(s^2-c^2))) ?
The solution to ln(((s^2+c^2)(s+a))/((s+b)(s^2-c^2))) is ln(s^2+c^2)+ln(s+a)-ln(s+b)-ln(s^2-c^2)