What is 3ln(x)+4ln(y)-6ln(z) ?

The solution to 3ln(x)+4ln(y)-6ln(z) is ln((x^3y^4)/(z^6))

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simplify 3ln(x)+4ln(y)-6ln(z)

simplify

3 ln (x) + 4 ln (y) - 6 ln (z)

ln (\frac{x ^{3} y ^{4}}{z ^{6}})

Solution steps

3 ln (x) + 4 ln (y) - 6 ln (z)

Apply log rule:

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

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

= ln (x^{3}) + 4 ln (y) - 6 ln (z)

Apply log rule:

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

4 ln (y) = ln (y^{4})

= ln (x^{3}) + ln (y^{4}) - 6 ln (z)

Apply log rule:

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

ln (x^{3}) + ln (y^{4}) = ln (x^{3} y^{4})

= ln (x^{3} y^{4}) - 6 ln (z)

Apply log rule:

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

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

= ln (x^{3} y^{4}) - ln (z^{6})

Apply log rule:

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

ln (x^{3} y^{4}) - ln (z^{6}) = ln (\frac{x ^{3} y ^{4}}{z ^{6}})

= ln (\frac{x ^{3} y ^{4}}{z ^{6}})

lo g_{6} (6 x)

ln (\frac{5}{13})

lo g_{b} (\frac{x ^{3} y}{z ^{4}})

lo g_{9} (5 x)

lo g_{9} (4 n p^{3})

What is 3ln(x)+4ln(y)-6ln(z) ?
The solution to 3ln(x)+4ln(y)-6ln(z) is ln((x^3y^4)/(z^6))