Thread: Exponent Question...

(x)^4/3 = 16


How do I find this?


Oh and more importantly, how do you do this?

(9)^x = 4th root (27) / 3

Originally Posted by JonathanEyoon

(x)^4/3 = 16

<-- Cube both sides

<-- Take the fourth root of both sides



What number is this? Well if you recall that ...



Of course, this is the principle value of the solution. You might note that x = -8 also solves the equation. (The easiest way to see this is to take and take the square root of both sides twice.) There are also two complex solutions. I can give you the general solution if you like; it's not much harder than what I derived here.

-Dan

Originally Posted by JonathanEyoon

(9)^x = 4th root (27) / 3

You want to get both sides of the equation to the same base. In this case, the easiest base to use is 3.

and , and , so...







Now we have that




-Dan