What is 1/2 ln(x)+9ln(y)-8ln(z) ?

The solution to 1/2 ln(x)+9ln(y)-8ln(z) is ln((x^{1/2}y^9)/(z^8))

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simplify 1/2 ln(x)+9ln(y)-8ln(z)

simplify

\frac{1}{2} ln (x) + 9 ln (y) - 8 ln (z)

ln (\frac{x ^{\frac{1}{2}} y ^{9}}{z ^{8}})

Solution steps

\frac{1}{2} ln (x) + 9 ln (y) - 8 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}}) + 9 ln (y) - 8 ln (z)

Apply log rule:

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

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

= ln (x^{\frac{1}{2}}) + ln (y^{9}) - 8 ln (z)

Apply log rule:

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

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

= ln (x^{\frac{1}{2}} y^{9}) - 8 ln (z)

Apply log rule:

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

8 ln (z) = ln (z^{8})

= ln (y^{9} x^{\frac{1}{2}}) - ln (z^{8})

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^{8}) = ln (\frac{y ^{9} x ^{\frac{1}{2}}}{z ^{8}})

= ln (\frac{x ^{\frac{1}{2}} y ^{9}}{z ^{8}})

ln (\frac{1}{2 π x})

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

ln (20 e)

- lo g_{10} (6 \cdot 1 0^{- 9})

lo g_{10} (2) + lo g_{10} (x + 3)

What is 1/2 ln(x)+9ln(y)-8ln(z) ?
The solution to 1/2 ln(x)+9ln(y)-8ln(z) is ln((x^{1/2}y^9)/(z^8))