What is ln(xa^{2x}e^{x^2}) ?

The solution to ln(xa^{2x}e^{x^2}) is ln(x)+2xln(a)+x^2

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simplify ln(xa^{2x}e^{x^2})

simplify

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

ln (x) + 2 x ln (a) + x^{2}

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

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

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

2 ln (x) - \frac{1}{3} ln (y)

lo g_{e} (\frac{3}{2})

lo g_{2} (\frac{c}{8})

lo g_{\frac{3}{2}} (9) + lo g_{\frac{3}{2}} (3) - lo g_{\frac{3}{2}} (8)

ln (\frac{e ^{2}}{13})

What is ln(xa^{2x}e^{x^2}) ?
The solution to ln(xa^{2x}e^{x^2}) is ln(x)+2xln(a)+x^2