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

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

Popular >

simplify ln((L^5M^2)/(sqrt(K)))

simplify

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)

ln (\frac{( x + 2 ) ^{4} y ^{\frac{1}{3}}}{( w - 1 ) ^{3}})

2 ln (x^{- 2}) - ln (y^{2})

lo g_{4} (x - 1) + lo g_{4} (2 x - 5)

ln (\frac{2 e}{3})

- lo g_{10} (5.2 \cdot 1 0^{- 4})

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