SOLUTION: How do I solve for t without using logs (1.46)^t=5

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Question 1035581: How do I solve for t without using logs
(1.46)^t=5
Found 2 solutions by josgarithmetic, Theo:
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
No. USE logarithms! Maybe, logarithms of whatever base you want, and also use Change of Base formula.

log%28b%2C%281.46%5Et%29%29=log%28b%2C5%29
t%2Alog%28b%2C1.46%29=log%28b%2C5%29
t=log%28b%2C5%29%2Flog%28b%2C1.46%29----------use Change of Base formula from here.

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
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.