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?
but their answer is ln 4/ (ln1.05- ln 0.8) ≈5.0979
how can i solve it the way they do?
-
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
======================================…
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
======================================…
-
?