What is ln(p)+2ln(q)+6ln(r) ?

The solution to ln(p)+2ln(q)+6ln(r) is ln(pq^2r^6)

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simplify ln(p)+2ln(q)+6ln(r)

simplify

ln (p) + 2 ln (q) + 6 ln (r)

ln (p q^{2} r^{6})

Solution steps

ln (p) + 2 ln (q) + 6 ln (r)

Apply log rule:

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

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

= ln (p) + ln (q^{2}) + 6 ln (r)

Apply log rule:

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

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

= ln (p q^{2}) + 6 ln (r)

Apply log rule:

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

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

= ln (p q^{2}) + ln (r^{6})

Apply log rule:

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

ln (p q^{2}) + ln (r^{6}) = ln (p q^{2} r^{6})

= ln (p q^{2} r^{6})

ln (15 \cdot e^{\frac{t}{t}})

4.75 + lo g_{10} (\frac{0.15}{0.7})

lo g_{2} (\frac{9 x ^{3} k}{5 y ^{4} z})

- \frac{1}{4} ln ∣ x + 3 ∣ + \frac{1}{4} ln ∣ x + 7 ∣

x \frac{\partial}{\partial x} (y) + ln (x y) + x

What is ln(p)+2ln(q)+6ln(r) ?
The solution to ln(p)+2ln(q)+6ln(r) is ln(pq^2r^6)