Question

Expand the logarithm.
ln((-3e^5)/(x^3))

Answer 1

ln(3) + 5 - 3ln(x) or 6.0986 - 3ln(x)

Explanation:

`ln((3e^(5) )/(x^3) )`

`ln((3e^(5) )/(x^3) )` =
`ln(3e^5)-ln(x^3)`, since ln(x/y) = ln(x)-ln(y)

`ln(3e^5)` = ln(3) +
`ln(e^5)`, since ln(xy) = ln(x) + ln(y)

`ln((3e^(5) )/(x^3) )` = ln(3) +
`ln(e^5)-ln(x^3)`

`ln((3e^(5) )/(x^3) )` =
`ln(3) + 5ln(e) -3ln(x)`, since ln(
`x^y`) = yln(x)

`ln((3e^(5) )/(x^3) )` = ln(3) + 5 -3ln(x) , since ln(e)=1

if needed further simplification,

ln(3) = 1.0986

ln(e) = 1

`ln((3e^(5) )/(x^3) )` = 6.0986 - 3ln(x)