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#1 2007-06-05 02:20:24

Liz
Guest

exponentials, soliving equations, simplify HELP PLEASE!!!!

Im stuck on these... can someone help?

A. fifteenth root of y^12 (simplify)

B.[x-2]>5       ([] means ab. value)

C. ((9x-8)/(36x^-4 times y^6))^-1/2

D. evaluate -5=logx

#2 2007-06-05 06:37:11

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: exponentials, soliving equations, simplify HELP PLEASE!!!!

A.

The fifteenth root of x can also be written as x^(1/15).
Therefore, the fifteenth root of y^12 = y^12^(1/15) = y^(12/15) = y^(4/5).

Or, if you prefer, the fourth root of y^5.

B.

The easiest way to solve abs questions is to split it into two parts.

|x-2| > 5
∴ x-2 > 5 or x-2 < -5

Solving each of these gives that x>7 or x<-3.

C.

This one isn't too difficult, it just involves a lot of stuff and so looks more complicated than it probably is. You just need to do it in lots of steps.

((9x-8)/(36x^-4 times y^6))^-1/2
((36y^6/x^4)/(9x-8))^1/2
(6y³/x²)/((9x-8)^1/2))
(6y³/x²√(9x-8))

I don't think it can be simplified further than that.

D.

Assuming the log is base 10, then we need to take both sides of the equation to powers of 10.

-5=logx
10^-5=10^logx
1/10^5=x
x = 0.00001.


Why did the vector cross the road?
It wanted to be normal.

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