A*log(b), Separating the two variables

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SUMMARY

The discussion centers on the equation log(D) - b*log(K) = b*log(z) - log(c) and the challenge of isolating D and K on one side. DonAntonio clarifies that using the property n*log_a(x) = log_a(x^n), the equation can be transformed to log(D/K^b) = log(z^b/c). However, this results in a function f(D,K,b) = g(b,z,c), which does not satisfy the original request for a separation of D and K from the other variables.

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fettapetta
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Hi!

I have a problem with the following equation:

log(D)-b*log(K) = b*log(z)-log(c)

I would like to get D and K on one side of the equal to sign, so that:

f(D,K) = g(b, c, z)

Is this possible?

Peter
 
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fettapetta said:
Hi!

I have a problem with the following equation:

log(D)-b*log(K) = b*log(z)-log(c)

I would like to get D and K on one side of the equal to sign, so that:

f(D,K) = g(b, c, z)

Is this possible?

Peter



Sure. It's always true that [itex]n\log_ax=\log_a(x^n)\,[/itex] , so [tex]\log D-b\log K=\log D-\log K^b=\log\left(\frac{D}{K^b}\right)[/tex]

DonAntonio
 
DonAntonio said:
Sure. It's always true that [itex]n\log_ax=\log_a(x^n)\,[/itex] , so [tex]\log D-b\log K=\log D-\log K^b=\log\left(\frac{D}{K^b}\right)[/tex]

DonAntonio

But this gives the function in the sense, f(D,K,b)=g(b,z,c), contrary to what the OP is asking.

I couldn't find a way to get only D and K on one side of the equality and rest of the variables on the other side, so I'm really curious about this one...
 

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