e^2x=4e^x+5

Question

solving for x by using logarithms 

Answer 1

Assuming you meant this: e^(2x) = 4e^x + 5

 

(e^x)^2 - 4(e^x) - 5 = 0

 

(e^x - 5)(e^x + 1) = 0

 

e^x = 5 or e^x = -1

 

e^x is always positive so e^x ≠ -1

 

e^x = 5

 

x = ln(5) ≈ 1.6094379124341

 

check:

 

e^(2(1.6094379124341)) ≈? 4e^(1.6094379124341) + 5

 

24.99999999999996 ≈ 24.99999999999998 √