Question

How do you solve `ln4-lnx=10`?

Answer 1

`x=4/(e^10)=~~1.82xx10^(-4)`

Explanation:

`ln(4) - ln(x) =10`

`color(white)("XXXXXXXXXX")`since `log(a/b) = log(a)-log(b)`
`rArr ln(4/x) = 10`

`color(white)("XXXXXXXXXX")`taking each side of the above as an exponent of `e`
`rArr 4/x = e^10`

`color(white)("XXXXXXXXXX")`algebraic simplification
`rArr x = 4/(e^10)`