Question

How do you simplify `2log 3+ log4-log6`?

Answer 1

`log(6)`

Explanation:

First, simplify `2log(3)` through the rule:

`b*log(a)=log(a^b)`

Thus, `2log(3)=log(3^2)=log(9)`.

Substitute this back into the original expression:

`=log(9)+log(4)-log(6)`

We can now use the following rule regarding the addition of logarithms (with the same base, which we do have in this scenario):

`log(a)+log(b)=log(ab)`

Thus the first two logarithms can be combined as follows:

`log(9)+log(4)=log(9*4)=log(36)`

Substituting this back into the expression, we obtain:

`=log(36)-log(6)`

Now, to subtract logarithms with the same base, we use the rule:

`log(a)-log(b)=log(a/b)`

Thus, the expression becomes

`=log(36/6)=color(blue)(log(6)`