What is 7ln(r)-6ln(u)-2ln(p) ?

The solution to 7ln(r)-6ln(u)-2ln(p) is ln((r^7)/(u^6p^2))

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simplify 7ln(r)-6ln(u)-2ln(p)

simplify

7 ln (r) - 6 ln (u) - 2 ln (p)

ln (\frac{r ^{7}}{u ^{6} p ^{2}})

Solution steps

7 ln (r) - 6 ln (u) - 2 ln (p)

Apply log rule:

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

7 ln (r) = ln (r^{7})

= ln (r^{7}) - 6 ln (u) - 2 ln (p)

Apply log rule:

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

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

= ln (r^{7}) - ln (u^{6}) - 2 ln (p)

Apply log rule:

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

ln (r^{7}) - ln (u^{6}) = ln (\frac{r ^{7}}{u ^{6}})

= ln (\frac{r ^{7}}{u ^{6}}) - 2 ln (p)

Apply log rule:

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

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

= ln (\frac{r ^{7}}{u ^{6}}) - ln (p^{2})

Apply log rule:

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

ln (\frac{r ^{7}}{u ^{6}}) - ln (p^{2}) = ln (\frac{\frac{r ^{7}}{u ^{6}}}{p ^{2}})

= ln (\frac{\frac{r ^{7}}{u ^{6}}}{p ^{2}})

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= ln (\frac{r ^{7}}{u ^{6} p ^{2}})

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What is 7ln(r)-6ln(u)-2ln(p) ?
The solution to 7ln(r)-6ln(u)-2ln(p) is ln((r^7)/(u^6p^2))