Question 419387
{{{ A (t)=30000*(1.08)^t }}}
{{{ 45000 = 30000*(1.08)^t }}}
Divide both sides by {{{30000}}}
{{{ 1.5 = (1.08)^t }}}
Take the log of both sides
{{{ log(1.5) = log(1.08^t) }}}
Now use the general rule:
{{{log(a^b) = b*log(a) }}}
{{{ log(1.5) = t*log(1.08) }}}
Divide both sides by {{{log(1.08)}}}
{{{ t = log(1.5)/log(1.08) }}}
{{{ t = .1761/.03342 }}}
{{{ t = 5.269 }}} 
To find months, {{{.269}}} yrs x {{{12}}} months/yr = 3.228
So far I have 5 yrs 3.228 months
To find days, {{{.228}}} months x {{{30}}} days/month = {{{6.84}}}
So, the time is 5 years, 3 months, 7 days
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check the answer:
{{{ 45000 = 30000*(1.08)^5.269 }}}
{{{1.5 = 1.50006}}} (by my calculator)
close enough