f4 math

1) 6e^x + e^-x = 5
Let k be e^x :
6k + 1/k = 5
6k^2 + 1 = 5k
6k^2 - 5k + 1 = 0
(2k - 1)(3k - 1) = 0
k = e^x = 1/2
x = In (1/2) = In (2^-1) = - In2
or e^x = 1/3
x = -In3
2) ln(2x^2 -14) - ln3x -2ln2 =0
In[2(x^2 - 7)] - In3x - In4 = 0
In { [2(x^2 - 7)] / (3x * 4) } = 0 = In 1
2(x^2 - 7)] / (3x * 4) = 1
x^2 - 7 = 6x
x^2 - 6x - 7 = 0
(x - 7)((x + 1) = 0
x = 7 or x = - 1(rejected)