What is ln(1/(a^2)x^ne^{b/a}) ?

The solution to ln(1/(a^2)x^ne^{b/a}) is nln(x)+b/a-2ln(a)

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simplify ln(1/(a^2)x^ne^{b/a})

simplify

ln (\frac{1}{a ^{2}} x^{n} e^{\frac{b}{a}})

n ln (x) + \frac{b}{a} - 2 ln (a)

Solution steps

ln (\frac{1}{a ^{2}} x^{n} e^{\frac{b}{a}})

Apply log rule:

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

ln (\frac{1}{a ^{2}} x^{n} e^{\frac{b}{a}}) = ln (\frac{1}{a ^{2}}) + ln (x^{n}) + ln (e^{\frac{b}{a}})

= ln (\frac{1}{a ^{2}}) + ln (x^{n}) + ln (e^{\frac{b}{a}})

Apply log rule:

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

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

= ln (\frac{1}{a ^{2}}) + n ln (x) + ln (e^{\frac{b}{a}})

Apply log rule:

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

ln (e^{\frac{b}{a}}) = \frac{b}{a} ln (e)

= ln (\frac{1}{a ^{2}}) + n ln (x) + \frac{b}{a} ln (e)

Apply log rule:

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

ln (\frac{1}{a ^{2}}) = ln (1) - ln (a^{2})

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

Apply log rule:

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

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

= ln (1) - 2 ln (a) + n ln (x) + \frac{b}{a} ln (e)

ln (1) = 0

\frac{b}{a} ln (e) = \frac{b}{a}

= 0 - 2 ln (a) + n ln (x) + \frac{b}{a}

0 - 2 ln (a) + n ln (x) + \frac{b}{a} = - 2 ln (a) + n ln (x) + \frac{b}{a}

= n ln (x) + \frac{b}{a} - 2 ln (a)

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What is ln(1/(a^2)x^ne^{b/a}) ?
The solution to ln(1/(a^2)x^ne^{b/a}) is nln(x)+b/a-2ln(a)