k from lnK

[905084274]

how do you find the K value from lnK. For example in problem 11.19 a and b from 6th edition? I never learned this and the solutions manual skips the process...

[ian_haliburton_1f]

when you have the ln of something isolated on one side of your equation, you can solve for what’s inside the ln by taking both sides and “exponentiating” them. This means you write
e^()=e^() with whatever was previously on each side of the equation in the parentheses. This works because e^(ln(x)) is just x due to logarithmic properties. So you are left with x=e^(), again with whatever was on the right side of the equation in the parentheses.

[Karan Thaker 2L]

You know how you have a -log(H+) to find pH, then to find H+ you raise 10 to the value of the pH? It's the similar thing... ln is just a log that has base e, so you take e and raise it to that power.

[A De Castro 14B 2H]

To exhibit the answers above, here's an example: if lnK = 0, then K = e⁰, making K = 1.

[Karan Thaker 2L]

think about it as bases. When we cancel a log, we do it by taking the base of "log" which is 10, and raising it to the power of the value. Here, it is the same principle, except the base is now "e' instead of 10.

[Alysa Rallistan 2G]

To get k alone you must raise lnK as the exponent for the number e, this essentially negates the ln and leaves k alone for you to solve