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Can you help me with the steps getting to the right side from the left of the equation.

logarithm equation

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  • $\begingroup$ Why dont you use Mathematica with Debug/Trace turned on? $\endgroup$
    – WolframFan
    Jan 11 '15 at 5:11
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    $\begingroup$ This is just l'Hospital's rule: Take the ratio of the derivative of the numerator and the derivative of the denominator on the left-hand side. $\endgroup$
    – David G. Stork
    Jan 11 '15 at 6:12
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f[x_] = (1 - 3^(1/x))/(1 + 3^(1/x));

Plot[f[x], {x, -1, 1}, Exclusions -> {x == 0}]

enter image description here

From the documentation for Limit,

Direction -> -1 takes variables to approach their limits by decreasing from larger values.

Limit[f[x], x -> 0, Direction -> -1]

-1

Using WolframAlpha from within Mathematica,

WolframAlpha["Limit[(1-3^(1/x))/(1+3^(1/x)), x -> 0, Direction -> -1]", 
  {{"Limit", 2}, "Content"}, PodStates -> {"Limit__Step-by-step solution"}]

enter image description here

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