How do you evaluate #log_4 (8)#?

1 Answer
KillerBunny · Tony B
May 7, 2018

#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#

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