Find logarithm fit to two points Say I have an equation $f(x) = \log_b(ax+1)$, where $a$ and $b$ are constants. If I have two distinct points $(x_1,y_1)$ and $(x_2, y_2)$, where $x_2 > x_1$ and $y_2 > y_1$, how can I find values for $a$ and $b$ such that $f(x_1) = y_1$, and $f(x_2) = y_2$?

Let $y_1=\log_{b}ax_1+1$ and $y_2=\log_{b}ax_2+1$ therefore$$b^{y_1}=ax_1+1\\b^{y_2}=ax_2+1$$then we have $$x_2b^{y_1}-x_1b^{y_2}=x_2-x_1$$ which doesn't have any analytic answer so doesn't for $a$
