What is ln((sqrt(z))/(x^5y)) ?

The solution to ln((sqrt(z))/(x^5y)) is ln(sqrt(z))-5ln(x)-ln(y)

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simplify ln((sqrt(z))/(x^5y))

simplify

ln (\frac{z}{x ^{5} y})

ln (z) - 5 ln (x) - ln (y)

Solution steps

ln (\frac{z}{x ^{5} y})

Apply log rule:

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

ln (\frac{z}{x ^{5} y}) = ln (z) - ln (x^{5} y)

= ln (z) - ln (x^{5} y)

Apply log rule:

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

ln (x^{5} y) = ln (x^{5}) + ln (y)

= ln (z) - (ln (x^{5}) + ln (y))

Apply log rule:

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

ln (x^{5}) = 5 ln (x)

= ln (z) - (5 ln (x) + ln (y))

- (5 ln (x) + ln (y)) : - 5 ln (x) - ln (y)

= ln (z) - 5 ln (x) - ln (y)

ln (8) + 3 ln (3)

ln (5.6 \cdot 7.8)

ln (9) + 2 ln (4)

ln (9) + 2 ln (2)

4 ln (3) + ln (2^{6})

What is ln((sqrt(z))/(x^5y)) ?
The solution to ln((sqrt(z))/(x^5y)) is ln(sqrt(z))-5ln(x)-ln(y)