Want to recode a logarithmic scale to linear

I have a set of variables measured on an ordinal scale. The format is LIKERT ranging from 1 ("Daily") to 6 ("less than once a year"). I think it is OK to analyze the data as interval scale data, then being able to use parametric tests. The underlying scale is logarithmic, meaning that 1 is "daily"; 2 represents half the value of 1; 3 represents half the value of 2; 4 represents half the value of 3, etc. So, if I look at it graphically it makes a descending curve with the "bow" on the downside.

I have used Compute variables > Arithmetic > ln10 to make the data linear, but I am unsure which way the "bow" is manipulated and in which direction the new scale goes. I have searched for "logarithmic recoding" on this forum and elsewhere, but can't find any answers.

Anyone in here who knows?
Users with solutions will get a "thanks".
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Ninja say what!?!
LOL. Umm...thanks for the "thanks"? I wonder if these "thanks" are even worth anything physically. It's nice to be recognized at least.

Anyways, in response to your question...I'm a little confused. You say that "the underlying scale is logarithmic". What does that mean? Do you mean that your variable follows a logarithmic distribution?

Also, what are you referring to when you say that you're making "the data linear"? In what sense are you making it linear? For linear regression? If you're unsure of which way the "bow" is manipulated, why not just graph out the transformed variable?