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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

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

lo g_{10} (100 y^{4} \times \frac{y + 5}{y - 5})

lo g_{4} (\frac{16}{x + 7})

\frac{3}{2} \cdot lo g_{3} (a) - \frac{1}{4} \cdot lo g_{3} (16 a^{2})

ln (\frac{e ^{x}}{1 + e ^{x}})

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