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Log Confusion...Please explain 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 


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


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Dr. Jonathan Y. | PhD, Science Tutor, Math, Technology, Test Prep, Chinese, R/W...PhD, Science Tutor, Math, Technology, Te...
4.9 4.9 (22 lesson ratings) (22)

Q:   lg(N^2+1)===??????????????? simplify

A:      (2+1)lgN



Q:  lg(N^2+1)/lgN ===?????????

A:    3lgN/lgN



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.

Yitzhak S. | Johns Hopkins Engineer, Specializing in Math and Science.Johns Hopkins Engineer, Specializing in ...
4.8 4.8 (4 lesson ratings) (4)

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.  

Jorge M. | Mathematics + Physics+ Computer ScienceMathematics + Physics+ Computer Science

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)


(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 log10(a)/log10(b)= logb(a)

For our given problem we are given:   log(N2+1)/log(N) = logN(N2+1)

If we have large N we can make an approximation: logN(N2+1)˜logN(N2) = 2