What is 3ln(5/2)+4ln(14/11) ?

The solution to 3ln(5/2)+4ln(14/11) is ln(600250/14641)

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simplify 3ln(5/2)+4ln(14/11)

simplify

3 ln (\frac{5}{2}) + 4 ln (\frac{14}{11})

ln (\frac{600250}{14641})

Decimal Notation

3.71352 \dots

Solution steps

3 ln (\frac{5}{2}) + 4 ln (\frac{14}{11})

Apply log rule:

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

3 ln (\frac{5}{2}) = ln ((\frac{5}{2})^{3})

= ln ((\frac{5}{2})^{3}) + 4 ln (\frac{14}{11})

Apply log rule:

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

4 ln (\frac{14}{11}) = ln ((\frac{14}{11})^{4})

= ln ((\frac{5}{2})^{3}) + ln ((\frac{14}{11})^{4})

Apply log rule:

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

ln ((\frac{5}{2})^{3}) + ln ((\frac{14}{11})^{4}) = ln ((\frac{5}{2})^{3} (\frac{14}{11})^{4})

= ln ((\frac{5}{2})^{3} (\frac{14}{11})^{4})

(\frac{5}{2})^{3} (\frac{14}{11})^{4} = \frac{600250}{14641}

= ln (\frac{600250}{14641})

ln (\frac{18}{22})

ln (5 e) - ln (1 0^{3}) + lo g_{2} (4^{2})

3 ln (x - 8) - 4 ln (x)

ln_{e^{2}} (4 e^{8})

- lo g_{10} (1.24 \cdot 1 0^{- 3})

What is 3ln(5/2)+4ln(14/11) ?
The solution to 3ln(5/2)+4ln(14/11) is ln(600250/14641)