What is expand ln((sqrt(x))/(e^x(x+3)^2)) ?

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

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expand ln((sqrt(x))/(e^x(x+3)^2))

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

= ln (x) - (x ln (e) + 2 ln (x + 3))

x ln (e) = x

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

- (x + 2 ln (x + 3)) : - x - 2 ln (x + 3)

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

ln (\frac{x ^{9} x ^{2} + 2}{( x + 2 ) ^{5}})

\frac{2.3 \cdot 9 \cdot 12}{150 \cdot 10800} \cdot ln (\frac{70}{30})

- ln (\frac{V}{N x}) - ln (\frac{bV}{N x})

ln (2 v^{2} + 1) - 2 ln (v^{2} + 1) - 2 ln (y)

ln (80) + ln (20)

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