What is ln((sqrt((x+5)^3))/(x^2+7x)) ?

The solution to ln((sqrt((x+5)^3))/(x^2+7x)) is ln(sqrt((x+5)^2)sqrt(x+5))-ln(x^2+7x)

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simplify ln((sqrt((x+5)^3))/(x^2+7x))

simplify

ln \frac{( x + 5 ) ^{3}}{x ^{2} + 7 x}

ln ((x + 5)^{2} x + 5) - ln (x^{2} + 7 x)

Solution steps

ln \frac{( x + 5 ) ^{3}}{x ^{2} + 7 x}

Apply log rule:

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

ln \frac{( x + 5 ) ^{3}}{x ^{2} + 7 x} = ln ((x + 5)^{3}) - ln (x^{2} + 7 x)

= ln ((x + 5)^{3}) - ln (x^{2} + 7 x)

(x + 5)^{3} = (x + 5)^{2} x + 5

= ln ((x + 5)^{2} x + 5) - ln (x^{2} + 7 x)

ln (\frac{21}{14})

ln (\frac{47}{50}) + (0.085) \cdot 0.05

\frac{1}{6} ln (\frac{75000}{600})

ln (\frac{2.63 \cdot 1 0 ^{- 30}}{2.949 \cdot 1 0 ^{- 76}})

\frac{1}{2} ln (7^{2} - 9) - \frac{1}{2} ln (5^{2} - 9)

What is ln((sqrt((x+5)^3))/(x^2+7x)) ?
The solution to ln((sqrt((x+5)^3))/(x^2+7x)) is ln(sqrt((x+5)^2)sqrt(x+5))-ln(x^2+7x)