simplify 4ln(6x^3)

Solution

simplify

4 ln (6 x^{3})

4 ln (6) + 12 ln (x)

Solution steps

4 ln (6 x^{3})

Apply log rule:

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

4 ln (6 x^{3}) = 4 ln (6) + 4 ln (x^{3})

= 4 ln (6) + 4 ln (x^{3})

Apply log rule:

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

ln (x^{3}) = 3 ln (x)

= 4 ln (6) + 4 \cdot 3 ln (x)

Multiply the numbers:

4 \cdot 3 = 12

= 4 ln (6) + 12 ln (x)

- lo g_{10} (9.82 \cdot 1 0^{- 9})

- lo g_{10} (7.93851 \cdot 1 0^{- 9})

ln (\frac{28}{25})

lo g_{7} (7 x^{9} y^{8})

- lo g_{10} (6.9 \cdot 1 0^{- 5})