SOLUTION: Evaluate the logarithmic expression 1-log[5]21

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Question 278554: Evaluate the logarithmic expression 1-log[5]21
Answer by jsmallt9(3296) About Me  (Show Source):
You can put this solution on YOUR website!
If the problem is:
1+-+log%285%2C+%2821%29%29
then, since no calculator I know "knows" base 5 logrithms, we need to convert this logarithm to a base our calculator does "know", like base 10 or base e (ln). There is a base conversion formula for this:
log%28a%2C+%28p%29%29+=+log%28b%2C+%28p%29%29%2Flog%28b%2C+%28a%29%29
Using this to convert the base 5 logarithm into a base 10 logarithm we get:
1+-+log%28%2821%29%29%2Flog%28%285%29%29
Now you can use your calculators to find the two logarithms, divide them and then subtract that from 1. (Be sure to use this order. Do not divide 21 by 5 first and then find the logarithm. That will not give you the correct answer.)