Question

Question #f8e12

Answer 1

`x=100e^-13.57~~1.278xx10^-4`

Explanation:

We will use the following properties of logarithms and exponents:

• `ln(xy) = ln(x)+ln(y)`
• `e^ln(x) = x`
• `e^-x = 1/e^x`
• `e^(x+y) = e^xe^y`

With those:

`ln(0.01x) = -13.57`

`=> ln(0.01)+ln(x) = -13.57`

`=> ln(x) = -13.57-ln(0.01)`

`=> e^ln(x) = e^(-13.57-ln(0.01))`

`:. x = e^(-(13.57+ln(0.01)))`

`=1/e^(13.57+ln(0.01))`

`=1/(e^13.57e^ln(0.01))`

`=1/(0.01e^13.57)`

`=100e^-13.57~~1.278xx10^-4`