What is ln((3x^2)/(x^2+4)) ?

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

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simplify ln((3x^2)/(x^2+4))

simplify

ln (\frac{3 x ^{2}}{x ^{2} + 4})

ln (3) + 2 ln (x) - ln (x^{2} + 4)

Solution steps

ln (\frac{3 x ^{2}}{x ^{2} + 4})

Apply log rule:

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

ln (\frac{3 x ^{2}}{x ^{2} + 4}) = ln (3 x^{2}) - ln (x^{2} + 4)

= ln (3 x^{2}) - ln (x^{2} + 4)

Apply log rule:

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

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

= ln (3) + ln (x^{2}) - ln (x^{2} + 4)

Apply log rule:

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

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

= ln (3) + 2 ln (x) - ln (x^{2} + 4)

- lo g_{10} (4.8 \cdot 1 0^{- 6})

\frac{9}{14} lo g_{10} (\frac{9}{14}) + \frac{5}{14} lo g_{\frac{5}{14}} (x)

ln (\frac{16}{3})

ln (\frac{300}{250})

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

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