How do you calculate #log_5 310#?

1 Answer
Sep 1, 2016

Answer:

#x = 3.564#

Explanation:

#log_5 310 = x#

Change to index form.

#5^x = 310 larr # variable is in the index log both sides.

#log5^x = log310#

#xlog5 = log310#

#x = log310/log5#

Using a calculator or tables gives:

#x = 3.564

Using the "Change of base law" gives the same result.

#log_a b = (logb)/(loga)#