Easy question...help?!
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Easy question...help?!

[From: ] [author: ] [Date: 12-05-22] [Hit: ]
but their answer isln 4/ (ln1.05- ln 0.8) ≈5.how can i solve it the way they do?-800 * (0.8)^t = 200 * (1.......
800(0,8^t=)200(1,05)^t => t=? I only know how to solve it like this: 4=(1,05/0,8)^t=> t= log...
but their answer is ln 4/ (ln1.05- ln 0.8) ≈5.0979
how can i solve it the way they do?

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800 * (0.8)^t = 200 * (1.05)^t -------------------------> I suppose this is your equation

Then,

You can simpify this as --->

800 / 200 = (1.05)^t / (0.8)^t

=> ( 1.05 / 0.8 )^t = 4

Take natural log both sides

=> ln (1.05 / 0.8)^t = ln 4

=> t * ln (1.05 / 0.8) = ln 4 ---------------------> Power Rule

=> t = ln 4 / ln (1.05 / 0.8) -----------------------> Value of t found out

Now, there is a rule of log which states that ln(a/b) = ln(a) - ln(b)

=> t = ln 4 / { ln(1.05) - ln(0.8) } --------------> ln(1.05 / 0.8) = ln(1.05 - 0.8), rule in log
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