re-arrange the equation to make (t) the subject. a=15.3 multiplied by 0.886 to the power of t .?

Question

no logarithms

Answer 1

If

a = 15.3*.886^t

then take the logarithm (common or natural) of both sides to get (I'll use natural logs)

ln(a) = ln(15.83) + t*ln(.886)

then rearrange to get

t = (ln(a)-ln(15.83))/ln(.886)


Doug

Answer 2

Using no logarithms, the expression cannot be rewritten with the t as the dependent variable. But if you are going to use the logs, then I would go with the first answer.

Answer 3

a = 15.3 * .886^t
(a/15.3) = .886^t
ln(a/15.3) = t(ln(.886))
t = (ln(a/15.3))/(ln(.886))

or

t = (ln((10a)/(153)))/(ln(886/1000))
t = (ln(10a) - ln(153))/(ln(443/500))
t = (ln(10) + ln(a) - ln(153))/(ln(443) - ln(500))