A*log(b), Separating the two variables

[fettapetta]

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

 

[DonAntonio]

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 $n\log_ax=\log_a(x^n)\,$ , so $$\log D-b\log K=\log D-\log K^b=\log\left(\frac{D}{K^b}\right)$$

DonAntonio

 

[Infinitum]

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

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...