Question

How do you evaluate `2^(log_2 37)`?

Answer 1

37

Explanation:

Let's first remember that a log is simply a different way to write an exponential expression:

`a^b=c <=> log_ac=b`

On the left hand side, we're saying that when we take the value `a` and multiply it by itself `b` times, we'll get the value `c`.

On the right hand side, we're saying that when we have a value `c`, we can arrive at that value by multiplying the value `a` `b` number of times.

So let's rewrite our expression in a different form:

`2^(log_2(37))=>log_2(c)=log_2(37)`

By observation, we can see that `c=37`.

Further, we can see that the exponential and the log are inverse relations of each other, and so when you apply one to the other, they cancel. This means, in this question, that the expression simplifies to 37.