What is 1/2 ln(x)+6ln(y)-9ln(z) ?

The solution to 1/2 ln(x)+6ln(y)-9ln(z) is ln((x^{1/2}y^6)/(z^9))

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simplify 1/2 ln(x)+6ln(y)-9ln(z)

simplify

\frac{1}{2} ln (x) + 6 ln (y) - 9 ln (z)

ln (\frac{x ^{\frac{1}{2}} y ^{6}}{z ^{9}})

Solution steps

\frac{1}{2} ln (x) + 6 ln (y) - 9 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}}) + 6 ln (y) - 9 ln (z)

Apply log rule:

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

6 ln (y) = ln (y^{6})

= ln (x^{\frac{1}{2}}) + ln (y^{6}) - 9 ln (z)

Apply log rule:

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

ln (x^{\frac{1}{2}}) + ln (y^{6}) = ln (y^{6} x^{\frac{1}{2}})

= ln (x^{\frac{1}{2}} y^{6}) - 9 ln (z)

Apply log rule:

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

9 ln (z) = ln (z^{9})

= ln (y^{6} x^{\frac{1}{2}}) - ln (z^{9})

Apply log rule:

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

ln (y^{6} x^{\frac{1}{2}}) - ln (z^{9}) = ln (\frac{y ^{6} x ^{\frac{1}{2}}}{z ^{9}})

= ln (\frac{x ^{\frac{1}{2}} y ^{6}}{z ^{9}})

lo g_{10} (\frac{- 5 ^{7} 2 ^{5}}{- 1 0 ^{8}})

ln (3 e^{7 x^{2} - 13 x + 5})

lo g_{b} (u^{5} v^{2})

- ln (x) + ln (c)

\frac{1}{3} lo g_{c} (x) + 4 lo g_{c} (y) - 3 lo g_{c} (x)

What is 1/2 ln(x)+6ln(y)-9ln(z) ?
The solution to 1/2 ln(x)+6ln(y)-9ln(z) is ln((x^{1/2}y^6)/(z^9))