Question 143204
Use logs

Given: {{{3^x=40}}}
Take the log of both sides
{{{log(3^x) = log(40)}}}
When using logs, if the term inside parens is raised to a power, then your can 'bring the power down' as a multiplier.
{{{x * log(3) = log(40) }}}
Now get out your handy calculator and find log(3) and log(40)
{{{x * (0.47712) = 1.602}}}
Now solve for x as a one step algebra simplification
{{{x = 3.3576}}}

Finally, check your answer using a calculator. Does 3^3.3576 = 40? Close enough!

For the second problem, use logs again. Except this time, use natural log (ln)
Given: {{{e^(0.04t)=1500}}}
Take the ln of both sides
{{{ln(e^(0.04t)) = ln(1500) }}}
The ln of a power of e, it just the power.
{{{0.04t = ln(1500) }}}
Whip out your calculator and find ln(1500)  (somebody help that man!)
{{{0.04t = 7.313}}}
{{{ t = 182.83}}}

Check your answer using the calculator. Does it check out? You bet it does,