While constructing some exponential curve, I have been trying to solve the following:
for $z$. I have tried using WolframAlpha, but it was unable to get any answer for $z$ within the standard computation limit, while Symbolab couldn't arrive at any answer. I'm not sure how to solve this by hand. I would initially try to reduce it to the form
but now, I'm not sure how to reduce this any further to get an answer for $z$.
In context, I can assume that $v$, $b$, $a$ and $m$ are positive real numbers, and that $a > m$.
I couldn't seem to be able to apply any log rules (since the bases would be different; e.g. $\log(x)+\log(y)=\log(xy)$ only holds when both $\log(x)$ and $\log(y)$ were to have the same base, which in this case they don't), so I don't know how to continue.