SOLUTION: find the value of log125^25

Question 718223: find the value of log125^25
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

The expression,as you posted it, is . If this is correct, then just type it into your calculator.
If the expression is: then...
- There is no exponent in this expression, even though it looks there is. The second 5 is not an exponent of the 125!! The 125 is the base of the logarithm and the 5 is the argument of the logarithm. Posting logarithms are difficult. To post a log like this, either
  - Use some English to help describe the log. For example, this one could be described as: "the base 125 log of 5"; or...
  - Teach yourself the syntax we use on algebra.com to get nice-looking logs like . Click on the "Show source" link above to see what I've typed to get these logs to look good.
- The expression represents the exponent one would put on 125 to get a result of 5. So this problem is asking us to figure out: What power of 125 is 5? Perhaps you already know the answer. Perhaps knowing that would help you figure out the answer. (It's not 3. 3 is the exponent we put on 5 to get 125. We're looking for the exponent to put on 125 to get 5.) If you still don't know the answer, then we can use to figure it out. We will use the change of base formula, to convert the base 125 log to an expression of base 5 logs:
  
  The numerator of this fraction is the exponent you put on a 5 to get 5. This should be 1, obviously. The denominator is the exponent you put on a 5 to get 125. From we know that this exponent is 3. So now we have:
  
  I hope this answer makes sense now. An exponent of 1/3, remember, means cube root.
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