What is expand ln((L^5M^2)/(sqrt(k))) ?

The solution to expand ln((L^5M^2)/(sqrt(k))) is 5ln(L)+2ln(M)-ln(sqrt(k))

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expand ln((L^5M^2)/(sqrt(k)))

expand

ln (\frac{L ^{5} M ^{2}}{k})

5 ln (L) + 2 ln (M) - ln (k)

Solution steps

ln (\frac{L ^{5} M ^{2}}{k})

Apply log rule:

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

ln (\frac{L ^{5} M ^{2}}{k}) = ln (L^{5} M^{2}) - ln (k)

= ln (L^{5} M^{2}) - ln (k)

Apply log rule:

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

ln (L^{5} M^{2}) = ln (L^{5}) + ln (M^{2})

= ln (L^{5}) + ln (M^{2}) - ln (k)

Apply log rule:

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

ln (L^{5}) = 5 ln (L)

= 5 ln (L) + ln (M^{2}) - ln (k)

Apply log rule:

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

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

= 5 ln (L) + 2 ln (M) - ln (k)

\frac{42}{3.9} ln (\frac{10}{3})

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

ln (4 e^{2 β} x^{2})

ln ((x + 1) 5^{x})

\frac{5}{2} + ln (\frac{5}{2})

What is expand ln((L^5M^2)/(sqrt(k))) ?
The solution to expand ln((L^5M^2)/(sqrt(k))) is 5ln(L)+2ln(M)-ln(sqrt(k))