What is expand ln(y=sqrt(x)*e^{x^2}*(x^2+10)^{10}) ?

The solution to expand ln(y=sqrt(x)*e^{x^2}*(x^2+10)^{10}) is ln(y)+ln(sqrt(x))+x^2+10ln(x^2+10)

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expand ln(y=sqrt(x)e^{x^2}(x^2+10)^{10})

expand

ln (y = x \cdot e^{x^{2}} \cdot (x^{2} + 10)^{10})

ln (y) + ln (x) + x^{2} + 10 ln (x^{2} + 10)

Solution steps

ln (y = x e^{x^{2}} (x^{2} + 10)^{10})

Apply log rule:

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

ln (y = x e^{x^{2}} (x^{2} + 10)^{10}) = ln (y) + ln (x) + ln (e^{x^{2}}) + ln ((x^{2} + 10)^{10})

= ln (y) + ln (x) + ln (e^{x^{2}}) + ln ((x^{2} + 10)^{10})

Apply log rule:

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

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

= ln (y) + ln (x) + x^{2} ln (e) + ln ((x^{2} + 10)^{10})

Apply log rule:

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

ln ((x^{2} + 10)^{10}) = 10 ln (x^{2} + 10)

= ln (y) + ln (x) + x^{2} ln (e) + 10 ln (x^{2} + 10)

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

= ln (y) + ln (x) + x^{2} + 10 ln (x^{2} + 10)

ln (ln (5) - 7 ln (10))

ln (\frac{2000}{1999}) 111

- 0.402 - \frac{0.05916}{2} lo g_{10} (\frac{0.5}{1})

4.184 \cdot ln (\frac{( 273.15 + 60 )}{( 273.15 + 18 )})

ln (x) + 6 ln (\frac{y + x}{x}) - 9 ln (\frac{y + 2 x}{x})

What is expand ln(y=sqrt(x)*e^{x^2}*(x^2+10)^{10}) ?
The solution to expand ln(y=sqrt(x)*e^{x^2}*(x^2+10)^{10}) is ln(y)+ln(sqrt(x))+x^2+10ln(x^2+10)