What is ln((xy^5)/(sqrt(z))) ?

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

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simplify ln((xy^5)/(sqrt(z)))

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

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61.54 ln (\frac{199}{1850})

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