Question

5(1.15)^t = 8(1.07)^t solve for t exactly if possible

Answer 1

If you could list your process as well that would be greatly appreciated

Answer 2

First i would get like terms on one side
5/8=(1.07/1.15)^t
Now to get rid of the exponent i would use the either log function (ln or log)
ln(5/8)=tln(1.07/1.15)
Then
(ln(5/8))/(ln(1.07/1.15))=t

Answer 3

Thanks!

Answer 4

you need to take the log of both sides and use some log laws

use base e logs

\[\ln(5\times(1.15)^t) = \ln(5 \times (1.07)^t)\]

this can be simplified to

\[\ln(5) + t \times \ln(1.15) = \ln(8) + t \times \ln(1.07)\]
or

\[t ( \ln(1.15) - \ln(1.07)) = \ln(8) - \ln(5)\]

that should help you solve for t