What is ln(x^{12}sqrt((y^{19))/(z^2)}) ?

The solution to ln(x^{12}sqrt((y^{19))/(z^2)}) is 12ln(x)+ln(sqrt((y^{19))/(z^2)})

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simplify ln(x^{12}sqrt((y^{19))/(z^2)})

simplify

ln (x^{12} \frac{y ^{19}}{z ^{2}})

12 ln (x) + ln (\frac{y ^{19}}{z ^{2}})

Solution steps

ln (x^{12} \frac{y ^{19}}{z ^{2}})

Apply log rule:

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

ln (x^{12} \frac{y ^{19}}{z ^{2}}) = ln (x^{12}) + ln (\frac{y ^{19}}{z ^{2}})

= ln (x^{12}) + ln (\frac{y ^{19}}{z ^{2}})

Apply log rule:

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

ln (x^{12}) = 12 ln (x)

= 12 ln (x) + ln (\frac{y ^{19}}{z ^{2}})

4 ln^{3} (- 6 e^{3} + \frac{9}{2})

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What is ln(x^{12}sqrt((y^{19))/(z^2)}) ?
The solution to ln(x^{12}sqrt((y^{19))/(z^2)}) is 12ln(x)+ln(sqrt((y^{19))/(z^2)})