1) ln(2t+1)=2-lnt Solve for t.

I just want to know whether I need to move lnt to the left side in order to solve the equation or can I just leave the equation as is and multiply both sides by e.

You don't multiply by e: you APPLY e at both sides. But first move ln t to the left side:
2) This problem has been bothering me for a while.

Differentiate y=10^tan(theta)

I tried to solving it earlier but I got stuck:

log10y=tan(theta)

So now can I use implicit differentiation?

Indeed: and etc. Tonio
Thank you!