How do I solve for t using logs

If you mean this:


12 = 24(0.84)t


Then rearrange:


t = \frac {12}{(24)(0.84)}


Now take the logarithm of both sides:


\log(t) = \log (\frac {12}{(24)(0.84)})


and apply the rules:

\log(ab) = \log (a) + \log (b) \\
\log(a/b) = \log (a) - \log (b)


Once you get the answer in terms of log(t) = x, then raise both sides to the power of 10, so you get


10^ {log(t)} = 10^x


and recall that


10^ {log(t)} = t


Hope this helps.