Question

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

Answer 1

Answer:

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

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

Step-by-step 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.