Question

How do I solve sinhx= -2 and sinhx= " alt="\frac{7}{2}" align="absmiddle" class="latex-formula">
and get the answer in logs?

Answer 1

Answer:

Step-by-step explanation:

1)

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

2)

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