MATH 121 Lecture 5: Unit 1 Section 5- Changing Log Bases

• School: Queen's University
• Department: Mathematics
• Course: MATH 121
• Professor: Alan Ableson

Document Summary

The calculators used for this class can only compute with log bases of 10 and e. to convert a log base, we can use the equation: To simplify the equation, we use the relationship between log and exponents. Take the log base 10 of this equation. Let log= log(cid:2869)(cid:2868)= log(cid:2869)(cid:2868) log(cid:2869)(cid:2868)= log(cid:2869)(cid:2868) log(cid:2869)(cid:2868) log(cid:2869)(cid:2868)= log(cid:3117)(cid:3116) = log. Example: numeric value. larger numeric value of x for 2 to equal 1000. Compute the numeric value of both the log values. Without exact calculation, determine which of (cid:2778)(cid:2777)(cid:2778)(cid:2777)(cid:2777)(cid:2777) and (cid:2779)(cid:2778)(cid:2777)(cid:2777)(cid:2777) has the larger log(cid:2869)(cid:2868)(cid:883)(cid:882)(cid:882)(cid:882) means that (cid:883)(cid:882)=(cid:883)(cid:882)(cid:882)(cid:882). This is simply 3, because 10 to the power of 3 is 1000. log(cid:2870)(cid:883)(cid:882)(cid:882)(cid:882) means that (cid:884)=(cid:883)(cid:882)(cid:882)(cid:882). From common sense, we already know that it would take a. Log(cid:2870)(cid:883)(cid:882)(cid:882)(cid:882) has the larger numeric value. log(cid:2869)(cid:2868)(cid:883)(cid:882)(cid:882)(cid:882) = 3 log(cid:2870)(cid:883)(cid:882)(cid:882)(cid:882) log(cid:2870)(cid:883)(cid:882)(cid:882)(cid:882)= log(cid:3117)(cid:3116)(cid:2869)(cid:2868)(cid:2868)(cid:2868) log(cid:3117)(cid:3116)(cid:2870) log(cid:2869)(cid:2868)(cid:884) (cid:885)(cid:882). (cid:885)(cid:882)(cid:883) log(cid:2869)(cid:2868)(cid:883)(cid:882)(cid:882)(cid:882) We can use the change of base formula.