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

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

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simplify 3ln(x)+4ln(yz)-ln(x^2y^2)

simplify

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

ln (x y^{2} z^{4})

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

ln (x^{3}) + ln ((yz)^{4}) = ln (x^{3} (yz)^{4})

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

(yz)^{4} = y^{4} z^{4}

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

Apply log rule:

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

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

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

Simplify

\frac{x ^{3} y ^{4} z ^{4}}{x ^{2} y ^{2}} : x y^{2} z^{4}

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

3 ln (3) - 4 ln (2) + 1

ln (x^{12} \frac{y ^{19}}{z ^{2}})

4 ln^{3} (- 6 e^{3} + \frac{9}{2})

2 lo g_{2} (a) + 3 lo g_{2} (b)

ln (\frac{x ^{7} cos ^{3} ( x )}{( x - 1 ) ^{\frac{9}{2}}})

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