Question 1035581
i believe logs were invented to spare you the trouble of having to do that without them.
using logs, your solution is done very simply.
(1.46)^t = 5 if and only if log1.46(5) = t
you would then use the log function of your calculator to get:
log(5) / log(1.46) = t
you would then solve for t to get t = 4.252861935.
you would then determine that 1.46^4.252861935 is equal to 5.


without logs, you would more then likely have to find the answer through iteration.


for example:


1.46^4 = 4.54371856
1.46^5 = 6.33829098
1.46^4.5 = 5.490196025.
1.46^4.25 = 4.994587628
1.46^4.26 = 5.013524778


you would keep iterating until you arrived at a solution that was within the degree of accuracy required, such as the answer is between 4.99999 and 5.00001.


at a minimum, you would need a calculator that allows you to perform these types of calculations.


more then likely, you would write a software program that did all the iterations for you and gave you the answer within the accuracy that you desired.


outside of that, i have no idea how you would solve a problem like that without the use of logs.