What is ln((sqrt(z))/(x^8y)) ?

The solution to ln((sqrt(z))/(x^8y)) is ln(sqrt(z))-8ln(x)-ln(y)

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simplify ln((sqrt(z))/(x^8y))

simplify

ln (\frac{z}{x ^{8} y})

ln (z) - 8 ln (x) - ln (y)

Solution steps

ln (\frac{z}{x ^{8} y})

Apply log rule:

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

ln (\frac{z}{x ^{8} y}) = ln (z) - ln (x^{8} y)

= ln (z) - ln (x^{8} y)

Apply log rule:

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

ln (x^{8} y) = ln (x^{8}) + ln (y)

= ln (z) - (ln (x^{8}) + ln (y))

Apply log rule:

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

ln (x^{8}) = 8 ln (x)

= ln (z) - (8 ln (x) + ln (y))

- (8 ln (x) + ln (y)) : - 8 ln (x) - ln (y)

= ln (z) - 8 ln (x) - ln (y)

ln (3) + ln (4) - ln (6)

- lo g_{10} (3.49 \cdot 1 0^{- 3})

ln (2 \cdot x) - x^{2} + 5

ln (\frac{66}{51}) \cdot 5

ln (r) + ln (t) + ln (r)

What is ln((sqrt(z))/(x^8y)) ?
The solution to ln((sqrt(z))/(x^8y)) is ln(sqrt(z))-8ln(x)-ln(y)