Log base c of 1 equals zero and log base c of b is nonzero because b does not equal one so log base c of 1 divided by log base c of b is equal to zero as is expected. Weve proven thechange of base formula. One other thing that we discussed was natural logarithms with a base of e.
For example 2 3 8.
A log start base a end base left parenthesis 18 right parenthesis dot log start base 3 end base left parenthesis a right parenthesis. The change of base formula for logarithms. You can also change the logarithm to any base x when you are using this property. Sal rewrites logarithmic expressions like 1logₐ4 or logₐ16log₂a using the change of base ruleWatch the next lesson.