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

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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*

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## Comments

I am not sure what you are asking. Are these three different problems?