What is ln(e^{sqrt(x+1)}x^2) ?

The solution to ln(e^{sqrt(x+1)}x^2) is sqrt(x+1)+2ln(x)

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simplify ln(e^{sqrt(x+1)}x^2)

simplify

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

x + 1 + 2 ln (x)

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

x + 1 ln (e) = x + 1

= x + 1 + 2 ln (x)

2 ln (2 + 1)

lo g_{10} (x y^{8})

lo g_{4} (11 b^{2} c)

ln (\frac{0.3}{0.25})

lo g_{10} (y z^{5})

What is ln(e^{sqrt(x+1)}x^2) ?
The solution to ln(e^{sqrt(x+1)}x^2) is sqrt(x+1)+2ln(x)