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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

- lo g_{10} (1.3 (1 0^{- 4}))

ln (6^{4})

ln (\frac{x + 3}{e ^{8 x}})

3 lo g_{8} (x + 2) - lo g_{8} (x)

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