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I have $$f(L) = M^{L-1} / (M+1) ^L $$ and $$ L = \log_M ((K+B)/A)$$

I am suppose to simply this to $$f = C(K+B)^{-b}$$ with $$ b = \dfrac{\ln(M+1) }{ \ln(M)}$$ for the top I have simplified $M^{L-1}$ to $\frac{K+B}{AM}$, but I have no idea how to simplify the bottom part. Some help would be great

NasuSama
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jam
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1 Answers1

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Something like $$a^{\log_a x}$$ is easy to simplify, this is what you have done for the top line. For the bottom you need to simplify $$a^{\log_b x}\ .$$ Try this: $$\eqalign{a^{\log_b x} &=(b^{\log_b a})^{\log_b x}\cr &=b^{(\log_b a)(\log_b x)}\cr &=(b^{\log_b x})^{\log_b a}\cr &=x^{\log_b a}\ .\cr}$$ I think this will give you what you want.

David
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