# Logarithmic scale

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## Logarithmic Scale

A scale where the same percentage of change between two data points (with respect to two other data points) may represent different, raw amounts of change. For example, a logarithmic scale of a stock may show a graph where a change from \$4 per share to \$8 per share is the same distance as a change from \$40 per share to \$80.

## Logarithmic scale.

On a logarithmic scale or graph, comparable percentage changes in the value of an investment, index, or average appear to be similar. However, the actual underlying change in value may be significantly different.

For example, a stock whose price increases during the year from \$25 to \$50 a share has the same percentage change as a stock whose price increases from \$100 to \$200 a share.

On a logarithmic scale, it's irrelevant that the dollar value of the second stock is four times the value of the first.

Similarly, the percentage change in the Dow Jones Industrial Average (DJIA) as it rose from 1,000 to 2,000 is comparable to the percentage change when it moved from 4,000 to 8,000.

References in periodicals archive ?
By Lemma 2.4 and max{[sigma]([f.sup.(k)]), [sigma]([A.sub.j][f.sup.(j)]), [sigma]([B.sub.j][f.sup.(j)]) (j = 0,1, ..., k - 1)} < n, for any given [epsilon](0 < 2[epsilon] < 1), there exists a set [E.sub.5] [subset] (1, +[infinity]) having finite logarithmic measure such that for all z with arg z = [theta] [member of] [0,2[pi])\H, [absolute value of z] = r [not member of] [0,1] [union] [E.sub.5], r [right arrow] +[infinity], we have
By Lemma 2.1, there exist a constant B > 0 and a set [E.sub.1] [subset] (1, +[infinity]) having finite logarithmic measure such that for all z satisfying [absolute value of z] = r [not member of] [0,1] [union] [E.sub.1], we have
By Lemma 2.2, there exist a sequence [{[r.sub.m]}.sub.m[member of]N], [r.sub.m] [right arrow] +[infinity] and a set [E.sub.2] of finite logarithmic measure such that the estimation
By Lemma 2.3, for any given [epsilon](0 < 2[epsilon] < min{1,n - [beta]}), there exists a set [E.sub.3] [subset] (1, +[infinity]) having finite logarithmic measure such that for all z with [absolute value of z] = r [not member of] [0,1] [union] [E.sub.3], r [right arrow] +[infinity], we have
By Lemma 2.4, for any given [epsilon](0 < 2[epsilon] < min {1, n - [beta]}), there exists a set [E.sub.5] [subset] (1, +[infinity] having finite logarithmic measure such that for all z with arg z = [theta] [member of] [0,2[pi])\H, [absolute value of z] = r [not member of] [0,1] [union] [E.sub.5], r [right arrow] +[infinity], we have
By Lemma 2.3, for any given [epsilon](0 < 2[epsilon] < min {1 - c/1 + c, n - [beta]}), there exists a set [E.sub.3] [subset] (1, +[infinity]) having finite logarithmic measure such that for all z with [absolute value of z] = r [not member of] [0,1] [union] [E.sub.3], r [right arrow] +[infinity], we have
By Lemma 2.4, for any given [epsilon](0 < 2[epsilon] < min{1 - c/1 + c, n - [beta]}), there exists a set [E.sub.5] [subset] (1, +[infinity]) having finite logarithmic measure such that for all z with arg z = [theta] [member of] [0,2[pi])\H, [absolute value of z] = r [not member of] [0,1] [union] [E.sub.5], r [right arrow] +[infinity], we have (3.31) and
By Lemma 2.3, for any given [epsilon](0 < 2[epsilon] < min {1, n - [beta]}) there exists a set [E.sub.3] [subset] (1, +[infinity]) having finite logarithmic measure such that for all z with [absolute value of z] = r [not member of] [0,1] [union] [E.sub.3], r [right arrow] +[infinity], we have (3.29) and (3.30).
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