Question

How do you evaluate `log_4 (8)`?

Answer 1

`1.5`

Explanation:

Since `4^1=4` and `4^2=16`, the answer lies between `1` and `2`. There is no much more that we can do by hands, so I'm assuming you meant something like "how to compute `log_4(8)` with a calulator?"

If so, you must use the rule that allows us to change the base:

`log_a(b) = log_c(b)/log_c(a)`

So, assuming your calculator has a button for the natural logarithm, you have

`log_4(8) = \frac{ln(8)}{ln(4)} = 1.5`