What is ln(x/((x+2)(x+3))) ?

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

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simplify ln(x/((x+2)(x+3)))

simplify

ln (\frac{x}{( x + 2 ) ( x + 3 )})

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

Solution steps

ln (\frac{x}{( x + 2 ) ( x + 3 )})

Apply log rule:

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

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

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

Apply log rule:

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

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

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

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

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

ln (\frac{x ^{2} x ^{2} + 3}{( x + 3 ) ^{8}})

ln (30) + 2 ln (y) + ln (x)

ln (\frac{1 + x}{x})

ln (8 e^{k^{4}})

ln (\frac{1560}{100})

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