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

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

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

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

ln (x) - \frac{1}{2} ln (x^{2} + 9)

4 ln (x) - ln (1 + x) + ln (1 - x)

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

ln (\frac{100 + 1.84}{1.84})

\frac{3}{2} (ln (11) - ln (3))

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