SOLUTION: log10^3 + log10^-7

Algebra ->  Algebra  -> Logarithm Solvers, Trainers and Word Problems -> SOLUTION: log10^3 + log10^-7      Log On

Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   

Question 226994: log10^3 + log10^-7
Answer by jsmallt9(3296) 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: