What is ln((sqrt(x^2+1))/((x+3)(x-2))) ?

The solution to ln((sqrt(x^2+1))/((x+3)(x-2))) is ln(sqrt(x^2+1))-ln(x+3)-ln(x-2)

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simplify ln((sqrt(x^2+1))/((x+3)(x-2)))

simplify

ln (\frac{x ^{2} + 1}{( x + 3 ) ( x - 2 )})

ln (x^{2} + 1) - ln (x + 3) - ln (x - 2)

Solution steps

ln (\frac{x ^{2} + 1}{( x + 3 ) ( x - 2 )})

Apply log rule:

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

ln (\frac{x ^{2} + 1}{( x + 3 ) ( x - 2 )}) = ln (x^{2} + 1) - ln ((x + 3) (x - 2))

= ln (x^{2} + 1) - ln ((x + 3) (x - 2))

Apply log rule:

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

ln ((x + 3) (x - 2)) = ln (x + 3) + ln (x - 2)

= ln (x^{2} + 1) - (ln (x + 3) + ln (x - 2))

- (ln (x + 3) + ln (x - 2)) : - ln (x + 3) - ln (x - 2)

= ln (x^{2} + 1) - ln (x + 3) - ln (x - 2)

- \frac{1}{0.07} ln (\frac{1}{100})

182000 \cdot [ln (0.77) - ln (1.3)]

ln (\frac{4 y ^{5}}{x ^{2}})

- lo g_{10} (2.9 \cdot 1 0^{- 3})

2 ln (3) - ln (2) - 2 ln (2)

What is ln((sqrt(x^2+1))/((x+3)(x-2))) ?
The solution to ln((sqrt(x^2+1))/((x+3)(x-2))) is ln(sqrt(x^2+1))-ln(x+3)-ln(x-2)