What is 1/2 ln(x)+2ln(y)-3ln(z) ?

The solution to 1/2 ln(x)+2ln(y)-3ln(z) is ln((x^{1/2}y^2)/(z^3))

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simplify 1/2 ln(x)+2ln(y)-3ln(z)

simplify

\frac{1}{2} ln (x) + 2 ln (y) - 3 ln (z)

ln (\frac{x ^{\frac{1}{2}} y ^{2}}{z ^{3}})

Solution steps

\frac{1}{2} ln (x) + 2 ln (y) - 3 ln (z)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{1}{2} ln (x) = ln (x^{\frac{1}{2}})

= ln (x^{\frac{1}{2}}) + 2 ln (y) - 3 ln (z)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= ln (x^{\frac{1}{2}}) + ln (y^{2}) - 3 ln (z)

Apply log rule:

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

ln (x^{\frac{1}{2}}) + ln (y^{2}) = ln (y^{2} x^{\frac{1}{2}})

= ln (x^{\frac{1}{2}} y^{2}) - 3 ln (z)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

3 ln (z) = ln (z^{3})

= ln (y^{2} x^{\frac{1}{2}}) - ln (z^{3})

Apply log rule:

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

ln (y^{2} x^{\frac{1}{2}}) - ln (z^{3}) = ln (\frac{y ^{2} x ^{\frac{1}{2}}}{z ^{3}})

= ln (\frac{x ^{\frac{1}{2}} y ^{2}}{z ^{3}})

lo g_{4} (x) - 3 lo g_{4} (y)

lo g_{3} (\frac{g}{27})

lo g_{10} (39284 x^{- 1.799})

lo g_{10} (\frac{4 ( 8 + x ) ^{2}}{x ^{5}})

What is 1/2 ln(x)+2ln(y)-3ln(z) ?
The solution to 1/2 ln(x)+2ln(y)-3ln(z) is ln((x^{1/2}y^2)/(z^3))