Question

PLEASE HURRY Write the equation as a single logarithm 3log(x-2)+2log(x+2)

Answer 1

The answer is c

Explanation:

on edge :)

Answer 2

`3\,log (x-2)+2\,log(x+2)` can be written as the single logarithm:

`log((x-2)^3\,(x+2)^2)`

Explanation:

Start by using in both terms of the expression the property of logarithm of a power that states:

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

so we recognize that the factor that multiplies each logarithmic expression, can be understood as the power of the argument of the function logarithm:

`3\,log(x-2)=log((x-2)^3)\\and\\2\,log(x+2)=log((x+2)^2)`

Then we use the property of logarithm of a product which states that:

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

So now we recognize the expression:

`log((x-2)^3)\,+\,log((x+2)^2)`

as the logarithm of the product:

`log((x-2)^3\,(x+2)^2)`

which is finally a single logarithm as requested.