Assist in rearrangment of equation that includes ln

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SUMMARY

The discussion centers on rearranging the equation T = ln(x/k) / (x - k) to solve for x. Two interpretations of the equation are presented: one where the logarithm is taken after dividing (T = ln(x/k) / (x - k)) and another where the division occurs before taking the logarithm (T = ln(x/y) / (x - k)). Clarifying the context and the correct interpretation is essential for providing accurate assistance in solving for x.

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  • Familiarity with algebraic manipulation techniques
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  • Research the properties of logarithms, focusing on their manipulation in equations
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T= ln x/k divided by (x-k)

I need to rearrange this equation to solve for x.

any suggestions?
 
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If you use log(x/y) = log(x) - log(y), then at the very least you can isolate all the terms that have x in them. What is the context of your problem and what have you tried so far?
 
Bgayn said:
T= ln x/k divided by (x-k)

I need to rearrange this equation to solve for x.

any suggestions?
Yes. Start by writing the equation unambiguously. What you wrote could mean either of these:
a)
$$T = \ln\left(\frac{x/k}{x - k}\right)$$
b)
$$T = \frac{\ln(x/y)}{x - k} $$

In other words, does the division happen before taking the log, or after? We can't help you if we don't know what the problem is.
 

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