So I'm studying for my finals which are next week and recently we've been doing a lot of log problems and the following problems I'm having troubles understanding. Any help would be great.
1) 10^(2x+1) = 4^(x-1)
2) 3^(2x+1) = 6^(x-3)
These first 2 I've tried using logs, but it doesn't get me anywhere in a position for isolating x to find out what x =, or maybe I'm just not seeing it but I've gotten to where:
(x-1)/(2x+1) = log 10 / log 4 for the first problem(#1), and I'm sure I'd get to the same point for #2 as well and not know what to do....
3. The number e...I'm very shady with this but were supposed to memorize all there is to know about e (just basic things) and I'm not sure on how these 2 statements are wrong
a) e is the greatest number a continuous growth will reach
b) e is the amount of money you get if you started with $1 and compounded the interest continuously
What I do know is that e is an asymptote for exponential growth where the base n is unknown, and it is the limit of when discrete growth turns continuous as n approaches infinity.
(If you could tell me anything else I should know, that would most likely help )
The last few nights I've been over homework for this intro to calculus class as well as many others but now I really need to get these problems because our teacher told us that there are only 20 or so problems which means they will require a lot of work