What is the general solution for 2cosh(2x)=5sinh(x)+3 ?

The general solution for 2cosh(2x)=5sinh(x)+3 is x=ln(0.83987…),x=ln(3.16657…)

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2cosh(2x)=5sinh(x)+3

2 cosh (2 x) = 5 sinh (x) + 3

x = ln (0.83987 \dots), x = ln (3.16657 \dots)

Solution steps

2 cosh (2 x) = 5 sinh (x) + 3

Rewrite using trig identities

2 \cdot \frac{e ^{2 x} + e ^{- 2 x}}{2} = 5 \cdot \frac{e ^{x} - e ^{- x}}{2} + 3

2 \cdot \frac{e ^{2 x} + e ^{- 2 x}}{2} = 5 \cdot \frac{e ^{x} - e ^{- x}}{2} + 3 : x = ln (0.83987 \dots), x = ln (3.16657 \dots)

x = ln (0.83987 \dots), x = ln (3.16657 \dots)

tan (x) = \frac{6.9}{6.6}

sin (x) - cos (x) = \frac{2}{2}

2 cos (x) = 7 - \frac{3}{cos ( x )}

- sin (x) + 2 = 0

csc (x) = - \frac{9}{7}, tan (x) > 0

What is the general solution for 2cosh(2x)=5sinh(x)+3 ?
The general solution for 2cosh(2x)=5sinh(x)+3 is x=ln(0.83987…),x=ln(3.16657…)