What is ln(((x+1)^2)/((x-3)sqrt(x+6))) ?

The solution to ln(((x+1)^2)/((x-3)sqrt(x+6))) is 2ln(x+1)-ln(x-3)-ln(sqrt(x+6))

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simplify ln(((x+1)^2)/((x-3)sqrt(x+6)))

simplify

ln (\frac{( x + 1 ) ^{2}}{( x - 3 ) x + 6})

2 ln (x + 1) - ln (x - 3) - ln (x + 6)

Solution steps

ln (\frac{( x + 1 ) ^{2}}{( x - 3 ) x + 6})

Apply log rule:

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

ln (\frac{( x + 1 ) ^{2}}{( x - 3 ) x + 6}) = ln ((x + 1)^{2}) - ln ((x - 3) x + 6)

= ln ((x + 1)^{2}) - ln ((x - 3) x + 6)

Apply log rule:

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

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

= 2 ln (x + 1) - ln ((x - 3) x + 6)

Apply log rule:

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

ln ((x - 3) x + 6) = ln (x - 3) + ln (x + 6)

= 2 ln (x + 1) - (ln (x - 3) + ln (x + 6))

- (ln (x - 3) + ln (x + 6)) : - ln (x - 3) - ln (x + 6)

= 2 ln (x + 1) - ln (x - 3) - ln (x + 6)

ln (\frac{103.5}{100})

\frac{- 3}{8} \cdot ln (- 8 x + 5) + ln (k)

lo g_{e} (a + b) + lo g_{e} (a - b) - 2 lo g_{e} (c)

ln (\frac{( 2 t + 1 ) ^{8}}{( 3 t - 1 ) ^{4}})

ln (\frac{e ^{x} - e ^{- x}}{2})

What is ln(((x+1)^2)/((x-3)sqrt(x+6))) ?
The solution to ln(((x+1)^2)/((x-3)sqrt(x+6))) is 2ln(x+1)-ln(x-3)-ln(sqrt(x+6))