What is 3(ln(e^{3x}(x+1))-ln(2x^2)) ?

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

\frac{1}{2} ln (\frac{17}{3})

- lo g_{10} (7 \cdot 1 0^{- 6})

ln (\frac{10}{6})

lo g_{5} (a) + \frac{1}{3} lo g_{5} (b)

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

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