Question 30867
{{{y = 2e^(3t-1)}}}
{{{ln(y) = ln(2e^(3t-1))}}}  introduce the natural log
{{{ln(y)= ln(2) + ln(e^(3t-1))}}} Product Rule of logs
{{{ln(y) = ln(2) + (3t-1)*ln(e)}}}  Ln of e is 1 as per definition of ln
{{{ln(y) = ln(2) + 3t-1}}} subtract the ln2 and add the 1 to both sides
{{{ln(y) - ln(2) +1 = 3t}}} divide both sides by 3 and use the quotient rule of logs
{{{t = (ln(y) - ln(2) +1)/3}}}

So Darryl yes your answer is correct but not in the most simple form