I've been provided with equations for known ranges of values in the past where the exponent of base 10 is based on an input voltage multiplied by a constant factor.
For example, we have an input voltage of 0-10 with a corresponding range of 1x10^-8 - 200, the equation for this is Output = 10^(1.030103*Input Voltage -8).
However I have a new range that I don't know how to calculate the value of the exponent.
I have an input voltage of 0-10 with a corresponding range of 0-9999. The equations format that has been used in the past is Output = 10^(x*Input Voltage - y).
For example, we have an input voltage of 0-10 with a corresponding range of 1x10^-8 - 200, the equation for this is Output = 10^(1.030103*Input Voltage -8).
How do I calculate x and y?
Thanks for any help.
You take the base $10$ logarithm and get two points on a straight line. You then use the two point formula for a line. Note that $10^x$ will never give an output of $0$. In your example, the output is supposed to range from $1\cdot 10^{-8}$ to $200$. Your followup has $0$ to $9999$.
For the original, you want $$\text{Output}=10^{x\cdot\text{input}-y}\\ \log_{10}\text{Output}=x\cdot\text{input}-y$$ Now you are given two points $(0,1\cdot 10^{-8}), (10,200)$ and you can plug them in to find $x,y$. The first gives you $y=8$ and you can solve for $x$ from $\log_{10}200\approx 2.30103=10\cdot x -8, x=1.030103$