SOLUTION: Rewrite the following expression using one or more properties of logarithms and evaluate without a calculator. log (1/10^-3)+log 10^4

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Rewrite the following expression using one or more properties of logarithms and evaluate without a calculator. log (1/10^-3)+log 10^4      Log On


   

Question 829896: Rewrite the following expression using one or more properties of logarithms and evaluate without a calculator.
log (1/10^-3)+log 10^4
Answer by LinnW(1048) About Me  (Show Source):
You can put this solution on YOUR website!
log+%28%281%2F%2810%5E-3%29%29%29%2Blog+%2810%5E4%29
Since %281%2F%2810%5E-3%29%29+=+%2810%5E3%29, the general rule is x%5E%28-1%29=%281%2Fx%29
log+%28%2810%5E3%29%29%2Blog+%28%2810%5E4%29%29
log+%28%2810%5E7%29%29
Since log+%28%2810%5E7%29%29 means the exponent on 10 that produces 10%5E7,
log+%28%2810%5E7%29%29=7