I am doing a chemistry prolem and I am stuck at:
0.00393 = x ^ -2.61 How do I find x?
2007-02-03 08:03:45 · 8 answers · asked by Sgt. Pepper 2 in Science & Mathematics ➔ Mathematics
Take the log of both sides:
log(0.00393) =log(x^-2.61) =-2.61(log x)
So x= 10^ [-(log 0.00393)/2.61] = about 8.35
2007-02-03 08:12:52 · answer #1 · answered by Jerry P 6 · 0⤊ 0⤋
This is a simple equation. As long as you do the same thing to both sides the equality is preserved. To reveal the value of x you need to have x^1 on one side. To change x ^-2.61 to x^1 you have to raise both sides to the power -1/2.61 i.e. the reciprocal of -2.61.
0.00393^-1/2.61 = (x^-2.61)^-1/2.61
8.3500 = x
2007-02-03 16:26:35 · answer #2 · answered by sandcrafter 1 · 0⤊ 0⤋
ok, just like taking the square root of both sides when there is an x^2, you can take the -2.61 root of both sides and find x.
If your calculator can't do that, then take the natural log of both sides, rewrite the right side as -2.61 ln x using logaritmic rules. So you have ln .00393 = -2.61 ln x. Divide both sides by -2.61 and you get -ln.00393/2.61 = ln x. Using another rule, you can say that e (the base of the log) raised to the power of ((-ln.00393)/2.61) = x. so your answer would be e^((-ln.00393)/2.61). Evil answer!!
2007-02-03 16:10:44 · answer #3 · answered by cheese4700 2 · 1⤊ 0⤋
Remember that with exponents, (a^b)^c = a^(bc). So if you raise both sides of the equation to the power of -1/(2.61), you get 0.00393 ^ (-1/(2.61)) = x ^ 1. This means you have to get your calculator to take 0.00393 to the power of -1/2.61.
You could also use the fact that log (a^b) = b log (a), so that log (0.00393) = -2.61 log x. So divide log(0.00393) by -2.61, and take 10 raised to this power.
2007-02-03 16:17:02 · answer #4 · answered by Anonymous · 0⤊ 0⤋
Note that x^(-2.61) is the same as 1/x^(2.61), so our equation is
0.00393 = 1/x^(2.61)
Multiply both sides by x^(2.61) gives us
0.00393 x^(2.61) = 1
Dividing both sides by 0.00393 gives us
x^(2.61) = 1/(0.00393)
At this point, you convert this to logarithmic form.
log[base 2.61](1/0.00393) = x
By the change of base formula, this equals
ln(2.61) / ln [ 1/0.00393 ] = x
Solve for this value and you have your x.
2007-02-03 16:10:26 · answer #5 · answered by Puggy 7 · 1⤊ 0⤋
x^ -2.61 = 0.00393
multiply everything by the power of -1/2.61
(x^-2.61)^(-1/2.61) = 0.00393^(-1/2.61)
x= 8.35004
2007-02-03 16:09:20 · answer #6 · answered by 7 · 1⤊ 0⤋
Take logs of both sides
log(0.00393) = -2.61*logx So log x = 2.1223 and x =8.35
2007-02-03 16:15:57 · answer #7 · answered by santmann2002 7 · 0⤊ 0⤋
Si, si, es muy facil, pero no hablo ingles.
"-2.61 root" 0.00393=
-0.119759872...
2007-02-03 16:11:05 · answer #8 · answered by Anonymous · 0⤊ 3⤋