Convert the following expressions to the indicated base.

Question

$a^{\frac{1}{\ln a}}$ using basa e, for $a is greater than 0$ and $a is not equal to 1$

Accepted Answer

Welcome back, everyone express the expression K to the power of we divided by L and K in terms of the natural base E or K being greater than zero and K not equal to one. And we are given for answer choices a hit to the power of Lneb eats the power of three, divided by L and KC eats the power of third and D keeps the power of three. So for this problem, we want to evaluate the expression in terms of the natural base E, right? And what we want to do is basically recall the formula. Whenever we have A to the power of X, we can express it as E to the power of X L ma. So what we're going to do is basically use this formula. For our example, we're given K to the power of three divided by LNK. So we're going to say that our A value is equal to K and our X value is going to be equal to the exponent we divided by L and K. Now when we apply the formula key to the power of three divided by LNK would be equal to E to the power of XX is equal to three divided by L and K multiplied by Ln of A. So Ln of K, now, if we carefully look at the exponent lnk those two cancel out and we end up with E to the power of third. So the answer to this problem would be option C which says eat the power of third. Thank you for watching.

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Convert the following expressions to the indicated base.

$a^{\frac{1}{\ln a}}$ using basa e, for $a is greater than 0$ and $a is not equal to 1$