simplify 5ln(*5l^2)

Solution

simplify

5 ln (\cdot 5 l^{2})

5 ln (5) + 10 ln (l)

Solution steps

5 ln (5 l^{2})

Apply log rule:

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

5 ln (5 l^{2}) = 5 ln (5) + 5 ln (l^{2})

= 5 ln (5) + 5 ln (l^{2})

Apply log rule:

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

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

= 5 ln (5) + 5 \cdot 2 ln (l)

Multiply the numbers:

5 \cdot 2 = 10

= 5 ln (5) + 10 ln (l)

2 lo g_{10} (\frac{5}{4})

\frac{1}{2} ln (\frac{4 3 + 6}{3})

ln (\frac{1.1 \cdot 1 0 ^{6}}{1.2 \cdot 1 0 ^{3}})

- lo g_{10} (1.46 \cdot 1 0^{- 9})

ln (4 y)