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log math, need help getting ride of e on both side of equation?
500e^0.4t = 800e^0.7t , solve for t
im not sure how to do this one, i know you have to take the natural log (ln) to get ride of the e
4 Answers
- 7 years agoFavorite Answer
First u must know that log e with base e =1
secondly, log ab=log a + log b
thirdly log a/b = log a - log b
and log a^b = b log a.
Now knowing these u can solve it.
Taking log with base e on both sides,
log 500 + log e^0.4t = log 800 + log e^0.7
which implies,
log 500 - log 800 = 0.7t - 0.4t
log 500/800 = 0.3t
log 5/8 = 0.3t
t = (log 5/8)/0.3
Source(s): Concept - 7 years ago
500/800 = e^(0.7t) / e^(0.4t)
5/8 = e^(0.7t - 0.4t)
5/8 = e^(0.3t)
ln(5/8) = 0.3 * t
ln(5/8) / 0.3 = t
t = -1.5666787641524518455031234371611
