$I_{sp}$ is inversely related to log of mass ratio if delta v is held constant, yes, but that's not how the rocket equation is usually applied.

The way the rocket equation is usually applied is that you have a delta-v requirement given by a particular mission -- for example, the 4100 m/s needed to get from low Earth orbit to lunar orbit. Your $v_e$ will be constrained by your available choices of rocket engine, and $m_f$ will be constrained by the payload you're trying to move.

Rearranging the equation to put $m_i$ on the left side is left as an algebraic exercise.

$I_{sp}$ is inversely related to log of mass ratio if delta v is held constant, yes, but that's not how the rocket equation is usually applied.

The way the rocket equation is usually applied is that you have a delta-v requirement given by a particular mission -- for example, the 4100 m/s needed to get from low Earth orbit to lunar orbit. Your $v_e$ will be constrained by your available choices of rocket engine, and $m_f$ will be constrained by the payload you're trying to move.

Rearranging the equation to solve for $m_i$ is left as an algebraic exercise.