What is 6ln(x)+4ln(y)-2ln(z) ?

The solution to 6ln(x)+4ln(y)-2ln(z) is ln((x^6y^4)/(z^2))

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simplify 6ln(x)+4ln(y)-2ln(z)

simplify

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

ln (\frac{x ^{6} y ^{4}}{z ^{2}})

Solution steps

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

Apply log rule:

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

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

= ln (x^{6}) + 4 ln (y) - 2 ln (z)

Apply log rule:

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

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

= ln (x^{6}) + ln (y^{4}) - 2 ln (z)

Apply log rule:

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

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

= ln (x^{6} y^{4}) - 2 ln (z)

Apply log rule:

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

2 ln (z) = ln (z^{2})

= ln (x^{6} y^{4}) - ln (z^{2})

Apply log rule:

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

ln (x^{6} y^{4}) - ln (z^{2}) = ln (\frac{x ^{6} y ^{4}}{z ^{2}})

= ln (\frac{x ^{6} y ^{4}}{z ^{2}})

lo g_{4} (\frac{2 x + 1}{3 y + 4})

\frac{1}{2} lo g_{b} (x) + 4 lo g_{b} (y) - 2 lo g_{b} (x)

1 - ln (\frac{2}{3})

lo g_{8} (\frac{3 x ^{3}}{( 4 ) ( 3 )})

lo g_{4} (x + 1) + lo g_{4} (x) - 4 lo g_{4} (4)

What is 6ln(x)+4ln(y)-2ln(z) ?
The solution to 6ln(x)+4ln(y)-2ln(z) is ln((x^6y^4)/(z^2))