What is 6ln(x)+2ln(y)-3ln(z) ?

The solution to 6ln(x)+2ln(y)-3ln(z) is ln((x^6y^2)/(z^3))

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simplify 6ln(x)+2ln(y)-3ln(z)

simplify

6 ln (x) + 2 ln (y) - 3 ln (z)

ln (\frac{x ^{6} y ^{2}}{z ^{3}})

Solution steps

6 ln (x) + 2 ln (y) - 3 ln (z)

Apply log rule:

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

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

= ln (x^{6}) + 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^{6}) + ln (y^{2}) - 3 ln (z)

Apply log rule:

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

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

= ln (x^{6} 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 (x^{6} y^{2}) - ln (z^{3})

Apply log rule:

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

ln (x^{6} y^{2}) - ln (z^{3}) = ln (\frac{x ^{6} y ^{2}}{z ^{3}})

= ln (\frac{x ^{6} y ^{2}}{z ^{3}})

lo g_{10} (12) - lo g_{10} (6)

lo g_{12} (12 x)

ln (\frac{5}{9})

What is 6ln(x)+2ln(y)-3ln(z) ?
The solution to 6ln(x)+2ln(y)-3ln(z) is ln((x^6y^2)/(z^3))