asinh from fraction

If I have $$\mathrm{asinh}\left(\frac{x}{2.8\cdot10^{-10}}\right) = 15$$ How can I calculate $$x$$? Should I use $$\mathrm{asinh} \, x = \ln(x+\sqrt{x^2+1})$$ Or something else?

• Why not apply $\sinh$ to both sides? – Arthur Mar 7 at 13:46
• (x/2.8*10^-10) = ASINH(15.0) you mean that? – JESUS_M Mar 7 at 13:49
• Let's say this, then. If you had the eqution $\operatorname{asinh}(y) = 15$, how would you solve it? Can you think of a single step that solves that equation? (Think about what $\operatorname{asinh}$ means. Not its formula, but its meaning / definition.) – Arthur Mar 7 at 13:50
• asinh(y) = ln(y +sqrt(y^2 + 1) = 15 then ln(y +sqrt(y^2 + 1) = 15 and I can calculate y – JESUS_M Mar 7 at 13:59
• I said not to use the formula. What is the main reason for $\operatorname{asinh}$ to exist? What is its purpose? – Arthur Mar 7 at 14:00

$$\ln\left(\frac{x}{\frac{14}{5}\cdot10^{-10}}+\sqrt{1+\left(\frac{x}{\frac{14}{5}\cdot10^{-10}}\right)^2}\right)=15\space\Longleftrightarrow\space x=\frac{7\sinh\left(15\right)}{25000000000}\tag1$$