Will reward 100pts and brainliest answer solve 6e^x-4e^-x=5 for x show your work

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)