Trying to convert a nasty logarithm into an

Jaylyn Villarreal

Jaylyn Villarreal

Answered question

2022-04-11

Trying to convert a nasty logarithm into an exponential
I have the following equation that I must express in terms of r:
ΔV=λ2πϵ0ln(rR)
This is a pretty tough one. I am not sure how to get the r out of the logarithm. I have tried to express the logarithm as ln(r)ln(R), , but I am not sure where to go from there, or where the coefficient should go. I know that ΔV goes up in the exponent...

Answer & Explanation

Quimpoah3b

Quimpoah3b

Beginner2022-04-12Added 13 answers

First solve for ln(rR). We get
ln(rR)=2πϵ0ΔVλ.
Now take the exponential of both sides, and it's nearly over.
Remark: Under other circumstances, your observation that ln(rR)=lnrlnR would be useful. Here it can be used, but there are quicker ways.

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