Can x be solved in this logarithmic equation?

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Say you have:
\frac{\log(x)}{r\log{x}} = y

r and y can be any given number.

Is there any way to solve this for x?

ie

\frac{\log(x)}{1.6\log{x}} = 20

I'm getting this because I'm trying to calculate f(x) = \frac{x}{a} where f(x) is of the form f(x) = cx^r
a > 1
 
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Dr-NiKoN said:
Say you have:
\frac{\log(x)}{r\log{x}} = y

r and y can be any given number.

Is there any way to solve this for x?

ie

\frac{\log(x)}{1.6\log{x}} = 20

I'm getting this because I'm trying to calculate f(x) = \frac{x}{a} where f(x) is of the form f(x) = cx^r
a > 1

I don't get this, sorry. correct me if i am wrong here but i have :

\frac {\log(x)}{r\log(x)} = y but doesn't the left hand side yield
\frac {1}{r} ?

i am missing the point here...you sure about this equation ?

marlon
 
Well, I'm trying to find x for f(x) = \frac{x}{a}

where f is of the form cx^r

I tried setting x = cx^r and taking the log to find x.

I was wondering if it was possible to find x that way, or maybe if there is another way?
 
cx^r = \frac {x}{a}
cx^r - \frac {x}{a} = 0
x * (cx^{r-1} - \frac {1}{a}) = 0
cx^{r-1} = \frac {1}{a} if x is not 0
x^{r-1} = \frac {1}{ca} if x is not 0
x = \sqrt [r - 1] {\frac {1}{ca}} if x is not 0


marlon
 
what do you say about that ?

marlon
 
Hm, there must be a more elegant way?
 
trust me , this is the most easy way out. working with log will make you go around in circles

marlon
 
Hehe, ok, works for me.

I'm finding myself confused looking for the more complex ways to solve stuff, when regular math will do the job. Oh well :)

thanks a lot.
 
If you did your logs properly it would also drop out:

cx^r=x/a

then, assuming x and every thing else for that matter, is positive,

logc + rlogx = logx - loga

(r-1)logx= -loga - log c

log x = -log(ac) * 1/(r-1)

or x = (ac)^{1/(1-r)

exactly as marlon showed without needing to use logs.
 

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