- Easy definition of inverse function is when the input of a function is the output of the other, and same the other way, output and input
- the inverse of f(x) is written f^-1(x)
- if you graph a function, the inverse would be symmetric about the y=x line
- log base 3 of x = 4 can be written as x=3^4, (david crockit story)
2. I'm alright with inverses and logs most of the time, but i was a bit confused when we began logs. nature logs bit confusing as well
One problem from the hw i had trouble with...
2^x + 2^-x = 5
when natural log comes into play, i have a brain fart
:D
Hey i know logs are kind of hard for me too!
ReplyDeleteAnd yeah that problem it's hard but when you see how to get to the answer you'll find out it was actually easy.
OK that problem involves the use of the quadratic formula remember :
ReplyDeletex= -b +and- square root(b^2 - 4ac) all this over /2a.
1) Since the exponent is negative you make the 2^-x into a fraction like this 1/2^x so it'll be positive.
2)Then you add the 2^x + 1/2^x by using the common denominator.
3) After that you multiply both sides by 2^x which is the common denominator. You'll be left with something like this:
4x^2+1=10^x so you move the 10^x to the ohter side making it negative and leaving in as
4x^2-10^x+1=0.
ok yOU CANNOT FACTOR SO U USE THE QUADRATIC FORMULA
Recall: a=4, b=-10, c=1
4.) Plug all the numbers in the formula , do the math and at the end you'll be left with something like this (thats what i got):
x=(10 +and- 2 squareroot of 21 over(/)8)
5.) Thats the final answer but remember the prooblem looks like this 2^x + 2^-x=5
so in order to get the exponents alone you use log2 (log base 2) because it's the inverse of the exponential so since you put log2 in front of everything the asnwer should have it too so at then end you answer is:
x= log2(10 +and- 2 squareroot of 21 over(/)8)
* I know it's a lot but hope it helps..!
What do you mean by "natural log comes into play?"
ReplyDeleteinverse wise? or natural logs in general?
All I can say is that "e" and "ln" are interrelated. So then that means the inverse of an "ln" function will have an "e" in it.
Well that problem doesnt have an "e"?
ReplyDeleteYeah it was confusing for me at first but just act like e is a simple number, not a complicated weird vortex