solve the equation 5coshx + 3sinhx = 4

Answer 1

sinhx = (e^x - e^-x)/2
and
coshx = (e^x + e^-x)/ , by definition.

then:
5coshx + 3sinhx = 4
5(e^x + e^-x)/2 + 3(e^x - e^-x)/2 = 4
5e^x + 5e^-x + 3e^x - 3e^-x = 8
8e^x + 2e^-x = 8
times e^x
8 (e^x)^2 + 2 = 8e^x
a quadratic, let a = e^x
8a^2 - 8a + 2 = 0
4a^2 - 4a + 1 = 0
(2a - 1)^2 = 0
a = 1/2

then e^x = 1/2
x = ln(1/2) = ln1 - ln2= -ln 2

x = -ln 2

Answer 2

Yeah amazing

Answer 3

5coshx+3sinhx=4