How do you condense $5 ln x - \frac{1}{2} ln y + 6 ln z$ $5 ln x - 1/2 ln y +6 ln z$ ?

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Answer 1 · 2018-08-03T10:12:50

$I n (\frac{x^{5} z^{6}}{\sqrt{y}})$ $In((x^5z^6)/sqrty)$

$5 I n x - \frac{1}{2} I n y + 6 I n z$ $5Inx-1/2Iny+6Inz$

$= I n x^{5} - I n \sqrt{y} + I n z^{6}$ $=Inx^5-Insqrty+Inz^6$

$= I n (\frac{x^{5}}{\sqrt{y}}) + I n z^{6}$ $=In(x^5/sqrty)+Inz^6$

$= I n (\frac{x^{5}}{\sqrt{y}} \times z^{6})$ $=In(x^5/sqrtytimesz^6)$

$= I n (\frac{x^{5} z^{6}}{\sqrt{y}})$ $=In((x^5z^6)/sqrty)$

Recall:
$a I n b = I n b^{a}$ $aInb=Inb^a$

$I n a + I n b = I n a b$ $Ina+Inb=In ab$

$I n a - I n b = I n (\frac{a}{b})$ $Ina-Inb=In(a/b)$

How do you condense 5lnx−12lny+6lnz5 ln x - 1/2 ln y +6 ln z ?