Answer:
x = ln(4/3)
Step-by-step explanation:
6e^x-4e^-x=5
We can subtract 5 from each side
6e^x-4e^-x -5 =5-5
6e^x-4e^-x-5=0
Multiply by e^x
e^x(6e^x-4e^-x-5)=0*e^x
Distribute
6e^2x - 4 e^0 -5e^x =0
Let m = e^x
6m^2 - 4 -5m =0
Rearrange
6m^2 -5m-4 =0
Factor
(2m+1) (3m-4)=0
Using the zero product property
2m+1 = 0 and 3m-4 =0
2m=-1 3m=4
m = -1/2 m = 4/3
Replace m with e^x
e^x = -1/2 and e^x = 4/3
But e^x cannot be negative so the first is not a solution
e^x = 4/3
Take the ln of both side
ln (e^x) = ln (4/3)
x = ln(4/3)
