How do you calculate #log_4 3.6# with a calculator?

1 Answer
Sep 3, 2016

Answer:

#x = log3.6/log4 = 0.924

Explanation:

#log_4 3.6#

In this log form, the question being asked is
"what index/power of 4 will give 3.6?"

As 3.6 is not one of the exact powers of 4, we will need a calculator.
Let's estimate first....

#4^1 = 4#, so the answer should be just less than 1.

Log form and index form are interchangeable.

#log_a b = c" "hArr" " a^c = b#

#log_4 3.6 = x " "hArr" " 4^x = 3.6#

#log 4^x = log 3.6 " "larr" log both sides"#

#xlog4 = log3.6#

#x = log3.6/log4 = 0.924 " "larr" the is what we expected"#