SOLUTION: solve for z: e^2z-1 = 3 sorry i dont really know what topic this is. im just trying to answer my math module :(

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: solve for z: e^2z-1 = 3 sorry i dont really know what topic this is. im just trying to answer my math module :(      Log On


   

Question 877594: solve for z: e^2z-1 = 3
sorry i dont really know what topic this is. im just trying to answer my math module :(
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming the equation is e%5E%282z-1%29+=+3


Use natural logs to isolate the exponent and then solve for z


e%5E%282z-1%29+=+3


ln%28e%5E%282z-1%29%29+=+ln%283%29


%282z-1%29ln%28e%29+=+ln%283%29


%282z-1%29%2A1+=+ln%283%29


2z-1+=+ln%283%29


2z+=+ln%283%29%2B1


z+=+%28ln%283%29%2B1%29%2F2 <--- Exact Answer


z+=+1.04930614433406 <--- Approximate Answer (use a calculator to evaluate, be sure to round appropriately if needed)