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in this lesson were going to talk about evaluating logs using the change of base formula so we know that log base 2 of 16 is equal to 4 because 2 to the fourth power is 16. but lets say if you dont know that heres how you can use the change of base formula to get the same answer but heres the formula log base a of b is equal to log of b divided by log of a and the reason why its called the change of base formula is because you can change the base originally the base is a but you can make it into any new base well call it c c could be 5 8 12. as long as these two are the same it doesnt really matter what c is the equation will work so log base 2 of 16 you can type it in your calculator as log 16 divided by log 2. now when you type it in your calculator like this its automatically going to make it base 10. so regardless of whatever the new base is you will still get the right answer so go ahead and type that in log 16 divided by log 2 and youll see that is equal to 4. try these
