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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

4 lo g_{b} (x) + 6 lo g_{b} (z)

lo g_{10} (\frac{x ^{2}}{y ^{4}})

lo g_{10} (2) - lo g_{10} (5)

lo g_{10} (\frac{ab}{c d})

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

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