What is ln((4sqrt(x))/(3+x)) ?

The solution to ln((4sqrt(x))/(3+x)) is 2ln(2)+ln(sqrt(x))-ln(3+x)

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simplify ln((4sqrt(x))/(3+x))

simplify

ln (\frac{4 x}{3 + x})

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

Solution steps

ln (\frac{4 x}{3 + x})

Apply log rule:

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

ln (\frac{4 x}{3 + x}) = ln (4 x) - ln (3 + x)

= ln (4 x) - ln (x + 3)

Apply log rule:

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

ln (4 x) = ln (4) + ln (x)

= ln (4) + ln (x) - ln (x + 3)

ln (4) = 2 ln (2)

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

ln (\frac{45 - 1}{1})

ln (10 e^{4})

5 ln (\frac{300}{100})

ln (\frac{x - 8}{x + 3})

\frac{1}{2} ln (\frac{4}{5})

What is ln((4sqrt(x))/(3+x)) ?
The solution to ln((4sqrt(x))/(3+x)) is 2ln(2)+ln(sqrt(x))-ln(3+x)