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I need to extract a real number I do not know from a chart of commodities prices that is presented in logarithmic form. I have a real number from a more recent date that I can use as comparison, but I don't have the foggiest idea how to use that to extract the unknown, or even how to write the question, so apologies for the word-problem format.

In 1875, the price of lead falls at 5.083467686422149 on the logarithmic scale. (Likely many irrelevant digits there and below, as this precision is much higher than my accuracy, but it should be close to correct.)

In 2000, the price of lead falls at 3.235277415351151 on the logarithmic scale.

The real number in 2000 was $400 a US Ton.

I need to know what the real number in 1875 was.

How do I calculate this?

Quinn
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1 Answers1

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May I interpret the question like this?

$logA/logC=3.23...$,

$A=400$,

$logB/logC=5.08...$,

so $B=?$

user771160
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  • Not sure where LogC comes into it, but that might be my lack of understanding of logarithms. Is that how you bring in the scale of the chart? If so, I think yes, but I still don't know how to put that into a calculator, physical or app. – Quinn Aug 15 '17 at 13:44
  • @Quinn well, I am not clear about the base of logarithm in your question, so I overcome by using an arbitrary constant base and divide by the original base's logarithm of the new base. So there is a log c, but that in fact is nothing to the question because we just need the ratio of log a/log b, not the exact value. That is my opinion. – user771160 Aug 15 '17 at 13:54