What is 3*ln(pq)+4*ln(pq^2) ?

The solution to 3*ln(pq)+4*ln(pq^2) is ln(p^7q^{11})

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simplify 3ln(pq)+4ln(pq^2)

simplify

3 \cdot ln (pq) + 4 \cdot ln (p q^{2})

ln (p^{7} q^{11})

Solution steps

3 ln (pq) + 4 ln (p q^{2})

Apply log rule:

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

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

= ln ((pq)^{3}) + 4 ln (p q^{2})

Apply log rule:

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

4 ln (p q^{2}) = ln ((p q^{2})^{4})

= ln ((pq)^{3}) + ln ((p q^{2})^{4})

Apply log rule:

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

ln ((pq)^{3}) + ln ((p q^{2})^{4}) = ln ((pq)^{3} (p q^{2})^{4})

= ln ((pq)^{3} (p q^{2})^{4})

Simplify

(pq)^{3} (p q^{2})^{4} : p^{7} q^{11}

= ln (p^{7} q^{11})

\frac{2}{6} lo g_{2} (\frac{2}{6}) + \frac{4}{6} lo g_{2} (\frac{4}{6})

lo g_{4} (2) + 2 lo g_{4} (9)

\frac{1}{5} [lo g_{4} (x) + lo g_{4} (3)] - [lo g_{4} (y)]

ln (x) + ln (x - 2)

lo g_{b} (\frac{x y}{z})

What is 3*ln(pq)+4*ln(pq^2) ?
The solution to 3*ln(pq)+4*ln(pq^2) is ln(p^7q^{11})