What is expand ln((r^2s^{11})/(t^{14)}) ?

The solution to expand ln((r^2s^{11})/(t^{14)}) is 2ln(r)+11ln(s)-14ln(t)

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expand ln((r^2s^{11})/(t^{14)})

expand

ln (\frac{r ^{2} s ^{11}}{t ^{14}})

2 ln (r) + 11 ln (s) - 14 ln (t)

Solution steps

ln (\frac{r ^{2} s ^{11}}{t ^{14}})

Apply log rule:

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

ln (\frac{r ^{2} s ^{11}}{t ^{14}}) = ln (r^{2} s^{11}) - ln (t^{14})

= ln (r^{2} s^{11}) - ln (t^{14})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (t^{14}) = 14 ln (t)

= ln (r^{2} s^{11}) - 14 ln (t)

Apply log rule:

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

ln (r^{2} s^{11}) = ln (r^{2}) + ln (s^{11})

= ln (r^{2}) + ln (s^{11}) - 14 ln (t)

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= 2 ln (r) + ln (s^{11}) - 14 ln (t)

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (s^{11}) = 11 ln (s)

= 2 ln (r) + 11 ln (s) - 14 ln (t)

\frac{1}{5} ln (x + 1) + \frac{4}{5} ln (x - 4)

5 lo g_{7} (y) - \frac{3}{5} lo g_{7} (z)

lo g_{10} (\frac{[ 1.02 ]}{[ 0.875 ]}) + 4.757

3 ln (x) - ln (y)

- lo g_{10} (5 \cdot 1 0^{5})

What is expand ln((r^2s^{11})/(t^{14)}) ?
The solution to expand ln((r^2s^{11})/(t^{14)}) is 2ln(r)+11ln(s)-14ln(t)