# How do you find the limit of #(a^t-1)/t# as #t->0#?

The limit is

We calculate the limit as follows

This is an indeterminate form, so apply l'Hôspital's rule

Taking logarithm on both sides

Differentiating

Therefore,

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To find the limit of (a^t-1)/t as t approaches 0, we can use L'Hôpital's rule. Taking the derivative of both the numerator and denominator with respect to t, we get (a^t * ln(a))/1. Evaluating this expression as t approaches 0, we have (a^0 * ln(a))/1, which simplifies to ln(a). Therefore, the limit of (a^t-1)/t as t approaches 0 is ln(a).

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