What is ln(x^{1/2}y^9)-ln(z^4) ?

The solution to ln(x^{1/2}y^9)-ln(z^4) is ln((x^{1/2}y^9)/(z^4))

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simplify ln(x^{1/2}y^9)-ln(z^4)

simplify

ln (x^{\frac{1}{2}} y^{9}) - ln (z^{4})

ln (\frac{x ^{\frac{1}{2}} y ^{9}}{z ^{4}})

Solution steps

ln (x^{\frac{1}{2}} y^{9}) - ln (z^{4})

Apply log rule:

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

ln (y^{9} x^{\frac{1}{2}}) - ln (z^{4}) = ln (\frac{y ^{9} x ^{\frac{1}{2}}}{z ^{4}})

= ln (\frac{x ^{\frac{1}{2}} y ^{9}}{z ^{4}})

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

ln ((x + 3)^{3}) - 2 ln (x) - 2 ln (x^{2} + 3 x)

lo g_{10} (7 x^{4})

7 lo g_{a} (m) - \frac{1}{3} lo g_{a} (r)

ln (\frac{29}{22.6})

What is ln(x^{1/2}y^9)-ln(z^4) ?
The solution to ln(x^{1/2}y^9)-ln(z^4) is ln((x^{1/2}y^9)/(z^4))