What is ln((x^4y^2)/(sqrt(z))) ?

The solution to ln((x^4y^2)/(sqrt(z))) is 4ln(x)+2ln(y)-ln(sqrt(z))

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simplify ln((x^4y^2)/(sqrt(z)))

simplify

ln (\frac{x ^{4} y ^{2}}{z})

4 ln (x) + 2 ln (y) - ln (z)

Solution steps

ln (\frac{x ^{4} y ^{2}}{z})

Apply log rule:

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

ln (\frac{x ^{4} y ^{2}}{z}) = ln (x^{4} y^{2}) - ln (z)

= ln (x^{4} y^{2}) - ln (z)

Apply log rule:

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

ln (x^{4} y^{2}) = ln (x^{4}) + ln (y^{2})

= ln (x^{4}) + ln (y^{2}) - ln (z)

Apply log rule:

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

ln (x^{4}) = 4 ln (x)

= 4 ln (x) + ln (y^{2}) - ln (z)

Apply log rule:

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

ln (y^{2}) = 2 ln (y)

= 4 ln (x) + 2 ln (y) - ln (z)

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What is ln((x^4y^2)/(sqrt(z))) ?
The solution to ln((x^4y^2)/(sqrt(z))) is 4ln(x)+2ln(y)-ln(sqrt(z))