How do you use the Change of Base Formula and a calculator to evaluate the logarithm #log_3 15#?

1 Answer
Jun 26, 2018

Answer:

#log_3 15=ln15/ln3=log15/log3~~2.465#

Explanation:

The change of base formula allows you to change bases of logarithms:
#log_b a=lna/lnb=log_c a/log_c b# where #c# is the new base of your choice.
With #a=15# and #b=3#, we get that #log_3 15=ln15/ln3=log15/log3# (#logx# is the base 10 logarithm) and using a calculator, it is approximately 2.465. The reason why we normally use the natural logarithm or the base 10 logarithm is that most calculators are equipped with these functions.