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Solve the equation 3sinh(2x) = 13 - 3e^(2x), answering in the form 0.5ln(k). where k is an integer

We know that: sinh(2x) = 2sinh(x)cosh(x) , therefore the equation becomes 6sinh(x)cosh(x) = 13 - 3e^2xWe also know that sinh(x) = 0.5*[e^x-e^-x] and that cosh(x) = 0.5*[e^x+e^-x], so the equation can be expanded into :
6/4[e^2x-e^-2x] = 13 - 3e^2x3e^2x -3e^-2x = 26 - 6e^2x
Rearrange and multiply by e^2x to get a quadratic in e^2x:9e^4x - 26e^2x - 3 = 0
Use Quadratic formula to find possible values for e^2x.Since e^2x must be greater than zero, only one answer is valid.Simply rearrange that answer to find the value of x.Answer: x = 0.5ln3

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Solve the equation 3sinh(2x) = 13 - 3e^(2x), answering in the form 0.5ln(k). where k is an integer

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