SOLUTION: log10^3 + log10^-7

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Question 226994: log10^3 + log10^-7
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Once you understand what logarithms represent this problem is extremely easy!

The expression log%28a%2C+%28b%29%29 represents "the exponent for a which makes b". In other words, "a to the log%28a%2C+%28b%29%29 power is b".

Applying this to your specific logs:
log%28%2810%5E3%29%29 represents the exponent for 10 which makes 10%5E3 which you can see is 3!
log%28%2810%5E%28-7%29%29%29 represents the exponent for 10 which makes 10%5E%28-7%29 which you can see is -7!
So
log%28%2810%5E3%29%29+%2B+log%28%2810%5E%28-7%29%29%29+=+3+%2B+%28-7%29+=+-4

Another way to do this is to use the following properties:
  • log%28a%2C+%28x%5Ey%29%29+=+y%2Alog%28a%2C+%28x%29%29
  • log%28a%2C+%28a%29%29+=+1

Using the properties, in the order listed, we get: