What is 3ln(x^3y)+2ln(yz^2) ?

The solution to 3ln(x^3y)+2ln(yz^2) is ln(x^9y^5z^4)

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simplify 3ln(x^3y)+2ln(yz^2)

simplify

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

ln (x^{9} y^{5} z^{4})

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

(x^{3} y)^{3} (y z^{2})^{2} : x^{9} y^{5} z^{4}

= ln (x^{9} y^{5} z^{4})

ln (5) + ln (x)

lo g_{4} (x^{2} - 9) - 6 lo g_{4} (x + 3)

- lo g_{b} (\frac{1}{7})

lo g_{5} (4) + lo g_{5} (\frac{4}{125})

ln (9 e)

What is 3ln(x^3y)+2ln(yz^2) ?
The solution to 3ln(x^3y)+2ln(yz^2) is ln(x^9y^5z^4)