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Evaluate lim(x to 0) (log(tan^(2)x)(tan^...

Evaluate `lim_(x to 0) (log_(tan^(2)x)(tan^(2)2x).`

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To evaluate the limit \( \lim_{x \to 0} \log_{\tan^2 x}(\tan^2 2x) \), we can follow these steps: ### Step 1: Rewrite the logarithm using the change of base formula Using the change of base formula for logarithms, we can express the limit as: \[ \lim_{x \to 0} \frac{\log(\tan^2 2x)}{\log(\tan^2 x)} \] ...
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