What is ln((3x^2)/((x+1)^{10)}) ?

The solution to ln((3x^2)/((x+1)^{10)}) is ln(3)+2ln(x)-10ln(x+1)

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simplify ln((3x^2)/((x+1)^{10)})

simplify

ln (\frac{3 x ^{2}}{( x + 1 ) ^{10}})

ln (3) + 2 ln (x) - 10 ln (x + 1)

Solution steps

ln (\frac{3 x ^{2}}{( x + 1 ) ^{10}})

Apply log rule:

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

ln (\frac{3 x ^{2}}{( x + 1 ) ^{10}}) = ln (3 x^{2}) - ln ((x + 1)^{10})

= ln (3 x^{2}) - ln ((x + 1)^{10})

Apply log rule:

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

ln ((x + 1)^{10}) = 10 ln (x + 1)

= ln (3 x^{2}) - 10 ln (x + 1)

Apply log rule:

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

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

= ln (3) + ln (x^{2}) - 10 ln (x + 1)

Apply log rule:

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

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

= ln (3) + 2 ln (x) - 10 ln (x + 1)

lo g_{10} (a^{5} b^{4})

lo g_{10} (\frac{( x ^{2} y )}{( w ^{5} z )})

lo g_{b} (\frac{x}{( yz ) ^{2}})

- lo g_{10} (3 \cdot 1 0^{- 5})

lo g_{4} (\frac{1}{8}) \cdot lo g_{8} (256)

What is ln((3x^2)/((x+1)^{10)}) ?
The solution to ln((3x^2)/((x+1)^{10)}) is ln(3)+2ln(x)-10ln(x+1)