What is ln((ex^2)/(x+1)) ?

The solution to ln((ex^2)/(x+1)) is 1+2ln(x)-ln(x+1)

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simplify ln((ex^2)/(x+1))

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (a) = 1

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

ln (x) + ln (x + 1)

\frac{1}{2} lo g_{10} (b) + 7 lo g_{10} (c)

ln (2 y)

lo g_{2} (x y)

5 lo g_{7} (2 x) - \frac{1}{3} lo g_{7} (5 x + 1)