How should logarithms be taught?
As one shape of a curve; in a notebook that demonstrates multiple methods of curve fitting with and without a logarithmic transform.<p>Logarithm: <a href="https:&#x2F;&#x2F;simple.wikipedia.org&#x2F;wiki&#x2F;Logarithm" rel="nofollow">https:&#x2F;&#x2F;simple.wikipedia.org&#x2F;wiki&#x2F;Logarithm</a> ; 
<a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Logarithm" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Logarithm</a>  :<p>&gt; <i>In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised, to produce that number x.</i><p>List of logarithmic identities: 
<a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;List_of_logarithmic_identities" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;List_of_logarithmic_identities</a><p>List of integrals of logarithmic functions: 
<a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;List_of_integrals_of_logarithmic_functions" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;List_of_integrals_of_logarithm...</a><p>As functions in a math library or a CAS that <i>should</i> implement the correct axioms correctly:<p>Sympy Docs &gt; Functions &gt; Contents: 
<a href="https:&#x2F;&#x2F;docs.sympy.org&#x2F;latest&#x2F;modules&#x2F;functions&#x2F;index.html#contents" rel="nofollow">https:&#x2F;&#x2F;docs.sympy.org&#x2F;latest&#x2F;modules&#x2F;functions&#x2F;index.html#c...</a><p>sympy.functions.elementary.exponential. log(x, base=e) == log(x)&#x2F;log(e), exp(), LambertW(), exp_polar() 
<a href="https:&#x2F;&#x2F;docs.sympy.org&#x2F;latest&#x2F;modules&#x2F;functions&#x2F;elementary.html#sympy-functions-elementary-exponential" rel="nofollow">https:&#x2F;&#x2F;docs.sympy.org&#x2F;latest&#x2F;modules&#x2F;functions&#x2F;elementary.h...</a><p>&quot;Exponential, Logarithmic and Trigonometric Integrals&quot; 
sympy.functions.special.error_functions. Ei: exponential integral, li: logarithmic integral, Li: offset logarithmic integral 
<a href="https:&#x2F;&#x2F;docs.sympy.org&#x2F;latest&#x2F;modules&#x2F;functions&#x2F;special.html#exponential-logarithmic-and-trigonometric-integrals" rel="nofollow">https:&#x2F;&#x2F;docs.sympy.org&#x2F;latest&#x2F;modules&#x2F;functions&#x2F;special.html...</a><p>numpy.log. log() base e, log2(), log10(), log1p(x) == log(1 + x)
<a href="https:&#x2F;&#x2F;numpy.org&#x2F;doc&#x2F;stable&#x2F;reference&#x2F;generated&#x2F;numpy.log.html" rel="nofollow">https:&#x2F;&#x2F;numpy.org&#x2F;doc&#x2F;stable&#x2F;reference&#x2F;generated&#x2F;numpy.log.h...</a><p>numpy.exp. exp(), expm1(x) == exp(x) - 1, exp2(x) == 2*x
<a href="https:&#x2F;&#x2F;numpy.org&#x2F;doc&#x2F;stable&#x2F;reference&#x2F;generated&#x2F;numpy.exp.html" rel="nofollow">https:&#x2F;&#x2F;numpy.org&#x2F;doc&#x2F;stable&#x2F;reference&#x2F;generated&#x2F;numpy.exp.h...</a><p>Khan Academy &gt; Algebra 2 &gt; Unit: Logarithms: 
<a href="https:&#x2F;&#x2F;www.khanacademy.org&#x2F;math&#x2F;algebra2&#x2F;x2ec2f6f830c9fb89:logs" rel="nofollow">https:&#x2F;&#x2F;www.khanacademy.org&#x2F;math&#x2F;algebra2&#x2F;x2ec2f6f830c9fb89:...</a><p>Khan Academy &gt; Algebra (all content) &gt; Unit: Exponential &amp; logarithmic functions
<a href="https:&#x2F;&#x2F;www.khanacademy.org&#x2F;math&#x2F;algebra-home&#x2F;alg-exp-and-log" rel="nofollow">https:&#x2F;&#x2F;www.khanacademy.org&#x2F;math&#x2F;algebra-home&#x2F;alg-exp-and-lo...</a><p>3blue1brown: &quot;Logarithm Fundamentals | Lockdown math ep. 6&quot;, &quot;What makes the natural log &quot;natural&quot;? | Lockdown math ep. 7&quot; <a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;playlist?list=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev" rel="nofollow">https:&#x2F;&#x2F;www.youtube.com&#x2F;playlist?list=PLZHQObOWTQDP5CVelJJ1b...</a><p>Feynmann Lectures 22-6: Algebra &gt; Imaginary Exponents: 
<a href="https:&#x2F;&#x2F;www.feynmanlectures.caltech.edu&#x2F;I_22.html#Ch22-S6" rel="nofollow">https:&#x2F;&#x2F;www.feynmanlectures.caltech.edu&#x2F;I_22.html#Ch22-S6</a><p>Power law functions: <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Power_law#Power-law_functions" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Power_law#Power-law_functions</a><p>In a two-body problem, 
of the 4-5 fundamental interactions: Gravity, Electroweak interaction, Strong interaction, Higgs interaction, a fifth force; which have <i>constant</i> exponential terms in their symbolic field descriptions? 
<a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Fundamental_interaction#The_interactions" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Fundamental_interaction#The_in...</a><p>Natural logs in natural systems:<p>Growth curve (biology) &gt; Exponential growth: 
<a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Growth_curve_(biology)#Exponential_growth" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Growth_curve_(biology)#Exponen...</a><p>Basic reproduction number: 
<a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Basic_reproduction_number" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Basic_reproduction_number</a><p>(... Growth hacking; awesome-grwoth-hacking: <a href="https:&#x2F;&#x2F;github.com&#x2F;bekatom&#x2F;awesome-growth-hacking" rel="nofollow">https:&#x2F;&#x2F;github.com&#x2F;bekatom&#x2F;awesome-growth-hacking</a> )<p>Metcalf&#x27;s law: <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Metcalfe's_law" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Metcalfe's_law</a><p>Moore&#x27;s law; doubling time:  <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Moore&#x27;s_law" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Moore&#x27;s_law</a><p>A block reward halving is a doubling of difficulty. What block reward difficulty schedule would be a sufficient inverse of Moore&#x27;s law?<p>A few queries:<p>logarithm cheatsheet 
<a href="https:&#x2F;&#x2F;www.google.com&#x2F;search?q=logarithm+cheatsheet" rel="nofollow">https:&#x2F;&#x2F;www.google.com&#x2F;search?q=logarithm+cheatsheet</a><p>logarithm on pinterest 
<a href="https:&#x2F;&#x2F;www.pinterest.com&#x2F;search&#x2F;pins&#x2F;?q=logarithm" rel="nofollow">https:&#x2F;&#x2F;www.pinterest.com&#x2F;search&#x2F;pins&#x2F;?q=logarithm</a><p>logarithm common core worksheet  
<a href="https:&#x2F;&#x2F;www.google.com&#x2F;search?q=logarithm+common+core+worksheet" rel="nofollow">https:&#x2F;&#x2F;www.google.com&#x2F;search?q=logarithm+common+core+worksh...</a><p>logarithm common core autograded exercise (... Khan Academy randomizes from a parametrized (?) test bank for unlimited retakes for <i>Mastery Learning</i>) 
<a href="https:&#x2F;&#x2F;www.google.com&#x2F;search?q=logarithm+common+core+autograded+exercise" rel="nofollow">https:&#x2F;&#x2F;www.google.com&#x2F;search?q=logarithm+common+core+autogr...</a>