How do you use the Change of Base Formula and a calculator to evaluate the logarithm #log_8 3#?

1 Answer
Jul 17, 2015

Answer:

I found: #log_8(3)=(ln(3))/(ln(8))=0.5283#

Explanation:

The change of base formula can be used to change the base of a log, say #b#, into another, say #c#, and can be written as:
#log_ba=log_ca/log_cb#
Normally you choose a new base that should be "easier" to use. In this case I would choose #e# that can be evaluated using a normal pocket calculator:
#log_8(3)=log_e(3)/(log_e(8))=(ln(3))/(ln(8))=0.5283#