Log Confusion...Please explain this equation

Question

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 

Answer 1

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.

Answer 2

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.  

Answer 3

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)