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welcome to this quick tutorial on change of base rule rewriting logarithms and writing some logarithmic numeric value in terms of some other logarithmic values so when we look at this problem we are trying to write the log base 2 of 140 in terms of x and y now one thing that I see here that I want to work with is the fact that we have a log base 2 so ideally we didnamp;#39;t want to get x and y both involving the log base 2 and ideally inside x and y we would like to have a prime number or some type of a simplified number overall with which to work so letamp;#39;s start with x equals log base 5 of 8 weamp;#39;re going to rewrite this given the fact that 8 is 2 cubed as x equals log base 5 of 2 cubed will pull the exponent out front x equals 3 log base 5 of 2 and weamp;#39;ll divide both sides by 3 so we get x over 3 is log base 5 of 2 now we will invoke our change of base rule so if we want to change the base here the log base 2 of 5 is the reciprocal of the log base 5 of 2 so this
