Expert: Paul Klarreich - 1/27/2008

Question
I want to solve for the ratio x/y or y/x for the logarithmic equation below where c is a constant.

log(y)/log(x)= c

Can I do this?
log(y) = clog(x)
exp(log(y)) = exp(clog(x))    <--- don't know this step
y= (x)exp(c)                <----- is this right?
y/x = exp(c)

Answer
Questioner:   Josey
Category:  Advanced Math
Private:  No
 
Subject:  How to calculate complex logarithm
Question:  I want to solve for the ratio x/y or y/x for the logarithmic equation below where c is a constant.
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Hi, Josey,


log(y)/log(x)= c

Can I do this?
log(y) = clog(x)   << -- yes, that's ok.

exp(log(y)) = exp(clog(x))    <--- don't know this step

This is correct, too.  But you could have said:

log(y) = clog(x) means

log y = log(x^c), and then

y = x^c

Now, if you MUST write  y/x, you can say:

y = x x^(c-1), and

y/x = x^(c-1)

And that's the best you can do, I think.

y= (x)exp(c)                <----- is this right?

No, it's not.
y/x = exp(c)
nor is this.