What is ln((U^{3/2}V)/(N^{5/2)}) ?

The solution to ln((U^{3/2}V)/(N^{5/2)}) is 3/2 ln(U)+ln(V)-5/2 ln(N)

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simplify ln((U^{3/2}V)/(N^{5/2)})

simplify

ln (\frac{U ^{\frac{3}{2}} V}{N ^{\frac{5}{2}}})

\frac{3}{2} ln (U) + ln (V) - \frac{5}{2} ln (N)

Solution steps

ln (\frac{U ^{\frac{3}{2}} V}{N ^{\frac{5}{2}}})

Apply log rule:

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

ln (\frac{U ^{\frac{3}{2}} V}{N ^{\frac{5}{2}}}) = ln (U^{\frac{3}{2}} V) - ln (N^{\frac{5}{2}})

= ln (V U^{\frac{3}{2}}) - ln (N^{\frac{5}{2}})

Apply log rule:

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

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

= ln (U^{\frac{3}{2}} V) - \frac{5}{2} ln (N)

Apply log rule:

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

ln (U^{\frac{3}{2}} V) = ln (U^{\frac{3}{2}}) + ln (V)

= ln (U^{\frac{3}{2}}) + ln (V) - \frac{5}{2} ln (N)

Apply log rule:

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

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

= \frac{3}{2} ln (U) + ln (V) - \frac{5}{2} ln (N)

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What is ln((U^{3/2}V)/(N^{5/2)}) ?
The solution to ln((U^{3/2}V)/(N^{5/2)}) is 3/2 ln(U)+ln(V)-5/2 ln(N)