Homework help to rearrange formula

Given the equation

${V}_{m}=u(\mathrm{ln}{m}_{0}-\mathrm{ln}{m}_{8})-g{t}_{f}$

I need to solve for ${m}_{0}$ Here is what I have but it looks messy and I feel like there is sometihng wrong or a better way

1st attempt

$\begin{array}{rl}& {V}_{m}=u(\mathrm{ln}{m}_{0}-\mathrm{ln}{m}_{8})-g{t}_{f}\\ & {V}_{m}=u(\mathrm{ln}{m}_{0})-u(\mathrm{ln}{m}_{8})-g{t}_{f}\\ & {V}_{m}=u(\mathrm{ln}{m}_{0})-u(\mathrm{ln}{m}_{8})-g{t}_{f}\\ & {V}_{m}=u(\mathrm{ln}{m}_{0})-u(\mathrm{ln}{m}_{8})-g{t}_{f}\\ & u(\mathrm{ln}{m}_{0})-u(\mathrm{ln}{m}_{8})-g{t}_{f}-{V}_{m}=0\\ & u(\mathrm{ln}{m}_{0})-u(\mathrm{ln}{m}_{8})-{V}_{m}=g{t}_{f}\\ & u(\mathrm{ln}{m}_{0})=g{t}_{f}+u(\mathrm{ln}{m}_{8})+{V}_{m}\\ & \mathrm{ln}{m}_{0}=(g{t}_{f}+u(\mathrm{ln}{m}_{8})+{V}_{m})\xf7u\\ & {e}^{(g{t}_{f}+u(\mathrm{ln}{m}_{8})+{V}_{m})\xf7u}={m}_{0}\end{array}$

2nd attempt - think this looks a little better but still not there yet

$\begin{array}{rl}& {V}_{m}=u(\mathrm{ln}\frac{{m}_{0}}{{m}_{8}})-g{t}_{f}\\ & {V}_{m}+g{t}_{f}=u(\mathrm{ln}\frac{{m}_{0}}{{m}_{8}})\\ & \frac{{V}_{m}+g{t}_{f}}{u}=\mathrm{ln}\frac{{m}_{0}}{{m}_{8}}\\ & {e}^{\frac{{V}_{m}+g{t}_{f}}{u}}=\frac{{m}_{0}}{{m}_{8}}\\ & {m}_{8}{e}^{\frac{{V}_{m}+g{t}_{f}}{u}}={m}_{0}\end{array}$

Given the equation

${V}_{m}=u(\mathrm{ln}{m}_{0}-\mathrm{ln}{m}_{8})-g{t}_{f}$

I need to solve for ${m}_{0}$ Here is what I have but it looks messy and I feel like there is sometihng wrong or a better way

1st attempt

$\begin{array}{rl}& {V}_{m}=u(\mathrm{ln}{m}_{0}-\mathrm{ln}{m}_{8})-g{t}_{f}\\ & {V}_{m}=u(\mathrm{ln}{m}_{0})-u(\mathrm{ln}{m}_{8})-g{t}_{f}\\ & {V}_{m}=u(\mathrm{ln}{m}_{0})-u(\mathrm{ln}{m}_{8})-g{t}_{f}\\ & {V}_{m}=u(\mathrm{ln}{m}_{0})-u(\mathrm{ln}{m}_{8})-g{t}_{f}\\ & u(\mathrm{ln}{m}_{0})-u(\mathrm{ln}{m}_{8})-g{t}_{f}-{V}_{m}=0\\ & u(\mathrm{ln}{m}_{0})-u(\mathrm{ln}{m}_{8})-{V}_{m}=g{t}_{f}\\ & u(\mathrm{ln}{m}_{0})=g{t}_{f}+u(\mathrm{ln}{m}_{8})+{V}_{m}\\ & \mathrm{ln}{m}_{0}=(g{t}_{f}+u(\mathrm{ln}{m}_{8})+{V}_{m})\xf7u\\ & {e}^{(g{t}_{f}+u(\mathrm{ln}{m}_{8})+{V}_{m})\xf7u}={m}_{0}\end{array}$

2nd attempt - think this looks a little better but still not there yet

$\begin{array}{rl}& {V}_{m}=u(\mathrm{ln}\frac{{m}_{0}}{{m}_{8}})-g{t}_{f}\\ & {V}_{m}+g{t}_{f}=u(\mathrm{ln}\frac{{m}_{0}}{{m}_{8}})\\ & \frac{{V}_{m}+g{t}_{f}}{u}=\mathrm{ln}\frac{{m}_{0}}{{m}_{8}}\\ & {e}^{\frac{{V}_{m}+g{t}_{f}}{u}}=\frac{{m}_{0}}{{m}_{8}}\\ & {m}_{8}{e}^{\frac{{V}_{m}+g{t}_{f}}{u}}={m}_{0}\end{array}$