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Logarithmic Method for Variable Powers
For:
$$y=f(x)^{g(x)}$$
taking logarithm gives:
$$\ln y=g(x)\ln f(x)$$
Therefore:
$$\lim y=e^{\lim[g(x)\ln f(x)]}$$
when the required limit exists.
Usage
- Used for variable-base and variable-exponent limits.
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Logarithmic Method for Variable Powers
For:
$$y=f(x)^{g(x)}$$
taking logarithm gives:
$$\ln y=g(x)\ln f(x)$$
Therefore:
$$\lim y=e^{\lim[g(x)\ln f(x)]}$$
when the required limit exists.
Usage
- Used for variable-base and variable-exponent limits.
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