How do you solve #lnx=-3#?

1 Answer
Jan 7, 2017

#color(magenta)"x = 0.050"#


Let's use the diagram below:

This photo tells us that the natural log (ln) and the exponential function (#e^(x)#) are inverses of each other, which means that if we raise the exponential function by ln of x, we can find x. But remember, if you do something on one side of the equation, you have to do the same thing on the opposite side of the equation.

In our case if we raise e to the ln x, we are just left with x on the left side since #e^(x)# and ln undo each other:

#cancele^(cancel"ln"x) = -3#

Now, we have to do the same thing on the right side and raise e to the -3 power like this:

#x = e^(-3)#

When you do that calculation, you obtain an approximate value of .050.

#x = 0.050#