SOLUTION: I dont understand 1.10^t = 1.4641 (1.10to the power of t (^=power of))

Algebra ->  Algebra  -> Exponents-negative-and-fractional -> SOLUTION: I dont understand 1.10^t = 1.4641 (1.10to the power of t (^=power of))      Log On

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Question 32668: I dont understand
1.10^t = 1.4641 (1.10to the power of t (^=power of))
Answer by kietra(57) About Me  (Show Source):
You can put this solution on YOUR website!
This problem uses a variable in an equation so the easier way to solve would be using logarithms. So, your equation1.1^t=1.4641 the first thing to do would be to take the log of both sides. log (1.1^t)= log(1.4641). Then, using the law of logs, we can take the exponent (t) in front of the log so now t(log 1.1) = log (1.4641). We want to isolate the variable next so divide log1.1 on both sides so t = (log1.4641)/(log1.1). Punch those in your calculator log 1.4641=.1655707 (approx) and log(1.1)=.0412937. Divide those two numbers (.1655707)/(.0412937) and t=4. If you check your problem, (1.1)^4=1.4641. Yep, it checks. Here's the problem again without the explanation:
1.1^t=1.4641
log (1.1^t)= log(1.4641)
t(log 1.1) = log (1.4641)
t = (log1.4641)/(log1.1)
t = (.1655707)/(.0412937)
t = 4