Hi, I', currently working on an audio envelope generator. The function is g = (exp ((ln s) * f) - 1) / (s - 1). How do I solve this for s? Any help would

#g = (exp((ln s) * f) - 1) / (s - 1)#, solve for s

1 Answer
Oct 10, 2017

We cannot form an explicit expression for #s#

Explanation:

We have:

# g = (exp((ln s) * f) - 1) / (s - 1) #
# \ \ = (exp(gln s) - 1) / (s - 1) #
# \ \ = (exp(ln (s^g)) - 1) / (s - 1) #
# \ \ = ( s^g - 1) / (s - 1) #

And so:

# (s-1) g = s^g - 1 #

# :. sg -g= s^g - 1 #

# :. s^g - sg = 1 - g#

And we cannot form an explicit expression for #s#