e ^ { x } - e ^ { - x } = 2 \quad ( M
Solve for M
M=\frac{e^{x}}{2}-\frac{1}{2e^{x}}
Solve for x
x=\ln(\sqrt{M^{2}+1}+M)
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2M=e^{x}-e^{-x}
Swap sides so that all variable terms are on the left hand side.
2M=-\frac{1}{e^{x}}+e^{x}
The equation is in standard form.
\frac{2M}{2}=\frac{-\frac{1}{e^{x}}+e^{x}}{2}
Divide both sides by 2.
M=\frac{-\frac{1}{e^{x}}+e^{x}}{2}
Dividing by 2 undoes the multiplication by 2.
M=\frac{e^{x}}{2}-\frac{1}{2e^{x}}
Divide e^{x}-\frac{1}{e^{x}} by 2.
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