How do you calculate #log_5 310#?

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Answer 1 · 2016-09-01T13:19:30

#x = 3.564#

#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)#