lg(N^2+1)===??????????????? simplify
lg(N^2+1)/lgN ===?????????
lg x/lg y===lg x - lg y (right or wrong ??????????)
Please simplify this equation
lg(N^2+1)===??????????????? simplify
lg(N^2+1)/lgN ===?????????
lg x/lg y===lg x - lg y (right or wrong ??????????)
Please simplify this equation
Q: lg(N^2+1)===??????????????? simplify
A: (2+1)lgN
=3lgN
Q: lg(N^2+1)/lgN ===?????????
A: 3lgN/lgN
=3.
Q: lg x/lg y===lg x - lg y (right or wrong ??????????)
A: wrong. lg x - lg y = lg(x/y) per rules. OR you can derive this rule yourself.
lg x/y = lg (x * y^-1)
= lg x + (-1) lg y
= lg x - lg y.
When in doubt, ALWAYS go back to the FIRST rule you learned.
If you typed the first one correctly, it does not simplify. The rules we have for logs:
log(x*y)= log(x) + log(y).
log(x/y)=log(x) - log(y).
log(x^y)= y*log(x).
log base b of x = log(x)/log(b)
The first one, as you can see, cannot simplify. We cannot use the rule with exponents, because the 1 is in the parentheses. We can't factor the inside, because N^2 + 1 does not factor. We are stuck.
The second one resembles our last rule. This is the same as Log base N of (N^2+1). Again, we are stuck because this does not factor.
The last one is wrong. You can confirm this by plugging in any two numbers into a calculator.
For example, log(100,000)/log(10)= 5. Log(100,000)-log(10)= 4. The rule is wrong.
It looks like you may have copied down the first couple of problems wrong though, so you may want to check that.
lg x/lg y===lg x - lg y (right or wrong ??????????)
This is wrong, but you have the right idea. The log property states that:
(lg x/y) = lg(x)-lg(y)
similarly,
(lg x* y)= lg(x)+lg(y)
Your assumptions are incorrect: log(x * y) = log (x) + log(y). The reverse is not true. In the same way, log (x/y) = log(x) - log(y). Again, the way you have it is not the same thing, and not correct.
You can check this by plugging in numbers.
If x is 1000, and y is 100, then according to you, log(1000)/log(100) would equal log(900). log(1000) = 3, log(100) = 2, and 3/2 = 1.5. Log(900) is NOT 1.5 (it is about 2.95).
HOWEVER log(1000/100) is equal to log(1000)-log(100). Log(10) = 1. Log(1000)-log(100)= 3-2=1.
You can confirm the rule for multiplication in the same way!
Since lg(1) = 0, by your logic, the answer to the first question would always be 0 (since anything times zero is zero). This is not true.
You're right, I did get it mixed up, sorry about the confusion John. Thanks for pointing that out Yitzhak! Jumped the gun on that one, I don't see any simple ways to simplify the given equation unless we can make an approximation as shown below.
We can use the base changing formula log_{10}(a)/log_{10}(b)= log_{b}(a)
For our given problem we are given: log(N^{2}+1)/log(N) = log_{N}(N^{2}+1)
If we have large N we can make an approximation: log_{N}(N^{2}+1)˜log_{N}(N^{2}) = 2
Sorry, *Jass*
Comments
I am not sure what you are asking. Are these three different problems?