What is the general solution for 4cosh(x)=7 ?

The general solution for 4cosh(x)=7 is x=ln((7+sqrt(33))/4),x=ln((7-sqrt(33))/4)

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4cosh(x)=7

4 cosh (x) = 7

x = ln (\frac{7 + 33}{4}), x = ln (\frac{7 - 33}{4})

Solution steps

4 cosh (x) = 7

Rewrite using trig identities

4 \cdot \frac{e ^{x} + e ^{- x}}{2} = 7

4 \cdot \frac{e ^{x} + e ^{- x}}{2} = 7 : x = ln (\frac{7 + 33}{4}), x = ln (\frac{7 - 33}{4})

x = ln (\frac{7 + 33}{4}), x = ln (\frac{7 - 33}{4})

2 tan^{2} (x) - tan (x) = 0

4 \cdot cos^{2} (x) - 3 = 0

3 tan (x) - 2 = - 1

x, 1 - cos (x) = 0

sin (a) = \frac{- 3}{2}

What is the general solution for 4cosh(x)=7 ?
The general solution for 4cosh(x)=7 is x=ln((7+sqrt(33))/4),x=ln((7-sqrt(33))/4)