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

1 Answer
Teddy
Jun 26, 2018

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.

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