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

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

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

expand

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

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

Solution steps

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (a) = 1

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

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

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

15 + 50 \cdot ln (\frac{4}{4 - 0.4 \cdot 4})

ln (\frac{9}{5}) - 3

(0 - ln (2)) - (2 ln (2) - ln (3))

- 20 ln (\frac{33}{7})

2 ln (1 + 2)

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