What is 1/2 ln(x)+6ln(y)-5ln(z) ?

The solution to 1/2 ln(x)+6ln(y)-5ln(z) is ln((x^{1/2}y^6)/(z^5))

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simplify 1/2 ln(x)+6ln(y)-5ln(z)

simplify

\frac{1}{2} ln (x) + 6 ln (y) - 5 ln (z)

ln (\frac{x ^{\frac{1}{2}} y ^{6}}{z ^{5}})

Solution steps

\frac{1}{2} ln (x) + 6 ln (y) - 5 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) - 5 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}) - 5 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}) - 5 ln (z)

Apply log rule:

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

5 ln (z) = ln (z^{5})

= ln (y^{6} x^{\frac{1}{2}}) - ln (z^{5})

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^{5}) = ln (\frac{y ^{6} x ^{\frac{1}{2}}}{z ^{5}})

= ln (\frac{x ^{\frac{1}{2}} y ^{6}}{z ^{5}})

- lo g_{10} (4.24 \cdot 1 0^{- 3})

lo g_{10} (y x^{9})

ln (7) + ln (x)

lo g_{10} (\frac{x ^{5}}{y ^{2}})

lo g_{10} (x^{2} + 2 x - 15) - lo g_{10} (x^{2} - 7 x + 12)

What is 1/2 ln(x)+6ln(y)-5ln(z) ?
The solution to 1/2 ln(x)+6ln(y)-5ln(z) is ln((x^{1/2}y^6)/(z^5))