Powharmonic series: Difference between revisions
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== log-base-b-of-a-powharmonic series == | == log-base-b-of-a-powharmonic series == | ||
[[File:Log-base-3-of-2-powharmonic series.png|thumb| | |||
log-base-3-of-2-powharmonic series | |||
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When we choose a <span><math>p</math></span> of the form <span><math>\log_{b}a</math></span>, the resulting scale will include every integer power of <span><math>a</math></span>, and the count of steps between each power of <span><math>a</math></span> will be equal to the next integer power of <span><math>b</math></span>. | When we choose a <span><math>p</math></span> of the form <span><math>\log_{b}a</math></span>, the resulting scale will include every integer power of <span><math>a</math></span>, and the count of steps between each power of <span><math>a</math></span> will be equal to the next integer power of <span><math>b</math></span>. | ||
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<math>3, 9, 27, 81… | <math>3, 9, 27, 81… | ||
</math> | </math>An equality involving exponents and logarithms helps us understand why: | ||
An equality involving exponents and logarithms helps us understand why: | |||
<math>\qquad x^{\log_{b}a} = a^{log_{b}x} | <math>\qquad x^{\log_{b}a} = a^{log_{b}x} | ||