Question

How do I solve sinhx= -2 and sinhx=
`(7)/(2)`
and get the answer in logs?

Answer 1

Explanation:

1)

`sinh(x)=-2\\\\(e^x-e^(-x))/(2) =-2\\\\e^(2x)-1=-4e^x\\\\(e^x)^2+4e^x-1=0\\\\\Delta=16+4=20\\\\e^x=(-4-√(5) )/(2) \ (exclude) \ or\ e^x=-2+√(5) \approx{0,236067977...}\\\\x=ln(-2+√(5) ) \approx{-1,443635475178...}\\\\`

2)

`sinh(x)=(7)/(2) \\\\(e^x-e^(-x))/(2) =(7)/(2) \\\\e^(2x)-1=7e^x\\\\(e^x)^2-7e^x-1=0\\\\\Delta=49+4=53\\\\e^x=(7-√(53) )/(2) \ (exclude) \ or\ e^x=(7+√(53))/(2) \approx{7,1400549...}\\\\x=ln(7+√(53) ) \approx{1,96572...}\\\\`