Week by week it is getting easier for me. We covered a good bit of informatio this week. I really thought the exponents was easy. The hardest part is just finding the same base. When it is b^x*b^y= b^x+y. When it s b^x/b^y= b^x-y. When it is (ab)^x= a^xb^y. When it is (a/b)^x= a^x/b^x. When it is (b^x)^y= b^xy. When it is b^x/y= y{b^x}.
To solve for an exponent
a. write as the same base
b. set exponents equal
c. solve for x
Simplfy
(b^2/a) ^-2
-b^-4/a^-2
-1/b^41/a^2
= a^2/b^4
With double fraction, you have to multiply the outsides by each other, and the insides byeach other.
Ex. (a^-2+b^-2)^-1
-(1/a^2+1/b^2)^-1
-(b^2/b^2*1/a^2+1/b^2*a^2/a^2)^-1
-(b^2/a^2b^2+a^2/a^2b^2)^-1
-(b^2+a^2/a^2b^2)^-1
=a^2b^2/b^2+a^2
This week we also covered logirythms (I doubt I spelled that correctly).
logb x=a
- b^a=x
Ex. log2 8=x
-2^x=8
x= 3
Domain of logs and ln = (0,infinity)
Range of logs and ln = (-infinity, infinity)
I do not fully understand the natural log thing (e) so if anyone can assist me, it will be well appreciated.
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The natural log thing is pretty easy. The base of a natural log is e. Say you have to solve ln^x=8. The base would be e in this log and the answer would be e^8=x.
ReplyDeleteto expand on what terrio said
ReplyDeleteE is always the base of natural log
so to put a natural log (Ln) into exponential form you would do the same thig as you would a regular logarithm
EX:
put Ln75=5 in exponential form
since the base of a natural log is e you would get
e^x = 75
the same concept goes for exanding from exponential form
Ex:
expand e^50
because you know e is the base of a natural log you know the answer would be
Ln50=x
Natural log is basically the same thing as a regular log. You would solve it the same way except that the base of a natural log is (e). Think of it like how when B-rob threw in alpha and beta symbols; you would solve it the same way and you dont have to freak out if u see something different.
ReplyDelete