(e^-x)=9/2 find x

e^-x = 9/2    this is equivalent to :

e^x = 2/9       take the ln of both sides

ln e^x = ln (2/ 9)    and we can write

x ( ln e ) = ln (2/ 9)       and  ln e = 1   ....  so  .....

x = ln (2/9)  ≈ -1.504