Question 421261
The problem is
{{{ e^(-.413t) = 5 }}}
It would be good if this equation was in the form
{{{ e^a = e^b }}}
Then {{{a}}} must equal {{{b}}}
To accomplish this, I'll say
{{{ 5 = e^x }}}
{{{ x = ln(5) }}}
Now I can use my calculator
{{{x = 1.6094}}}
so,
{{{e^(-.413t) = e^1.6094}}}
{{{ -.413t = 1.6094}}}
{{{ t = -3.897 }}} answer
check answer:
{{{ e^(-.413t) = 5 }}}
{{{ e^(-.413*(-3.897)) = 5 }}}
{{{ e^1.609 = 5}}}
{{{ 5.00 = 5}}}