What is 4ln(x)+2ln(y)-3ln(z) ?

The solution to 4ln(x)+2ln(y)-3ln(z) is ln((x^4y^2)/(z^3))

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simplify 4ln(x)+2ln(y)-3ln(z)

simplify

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

ln (\frac{x ^{4} y ^{2}}{z ^{3}})

Solution steps

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

Apply log rule:

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

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

= ln (x^{4}) + 2 ln (y) - 3 ln (z)

Apply log rule:

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

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

= ln (x^{4}) + ln (y^{2}) - 3 ln (z)

Apply log rule:

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

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

= ln (x^{4} y^{2}) - 3 ln (z)

Apply log rule:

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

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

= ln (x^{4} y^{2}) - ln (z^{3})

Apply log rule:

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

ln (x^{4} y^{2}) - ln (z^{3}) = ln (\frac{x ^{4} y ^{2}}{z ^{3}})

= ln (\frac{x ^{4} y ^{2}}{z ^{3}})

lo g_{10} (x + 1) + lo g_{10} (2 x) - lo g_{10} (x)

6 lo g_{3} (u) + 5 lo g_{3} (v)

lo g_{d} (u^{3} v^{2})

6 lo g_{6} (x) - 5 lo g_{6} (y)

ln (\frac{27}{4})

What is 4ln(x)+2ln(y)-3ln(z) ?
The solution to 4ln(x)+2ln(y)-3ln(z) is ln((x^4y^2)/(z^3))