Given this function:
$$\frac{1.0}{1024.0} + \frac{x}{100.0} * \frac{1023.0}{1024.0} = y$$ $$10 * \frac{\log_{10}(y)}{\log_{10}(2)} = z$$ $$z * 100 = a$$
So f(0) = 10000 & f(100) = 0.
I need to find the inverse. It would be really helpful if I could see the steps. Thanks!
I don't see where f() is defined, so I'll just solve the one equation with a log in it and hope that helps you...
$$10*\frac{log_{10}(y)}{log_{10}(2)}=z$$ using the change of bases formula $$10*log_{2}(y)=z$$ $$log_{2}(y)=\frac{z}{10}$$ $$2^{log_{2}(y)}=2^\left(\frac{z}{10}\right)$$ $$y=2^\left(\frac{z}{10}\right)$$
in terms of a
$$y=2^{10a}$$
hope that helps!!!
oops, just saw your note!
$$a=100z$$ $$a=100*10*log_{2}(y)$$ $$a=1000*log_{2}\left(\frac{1}{1024}+\frac{1023}{102400}*x\right)$$