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in this video were going to focus on solving logarithmic equations with different bases now the most important thing that you need to know for this video is the change of base formula lets say if you have log base a of b this is equal to log b divided by log a but with a different base you can change it to any other base were going to call it c c could be any number it could be 2 5 8. as long as its the same the equation holds true so thats the change of base formula so lets say for example if i wish to evaluate log base 9 of 27 i can write it as log 27 divided by log 9. now what base do i want to use do i want to use 2 4 8 3 7 out of all the numbers to pick what number should i use now what number goes into nine and twenty seven the best number is three nine and twenty seven are both divisible by three now what is log base three of nine what is that equal to how many threes do you have to multiply to get to nine three times three is nine you have to multiply two threes so log b