SOLUTION: Hello! Use the Laws of Logarithms to expand the expression. Use the Laws of Logarithms to expand the expression. log(10^x/x(x^2+5)(x^7+6)) thanks for your help!

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Hello! Use the Laws of Logarithms to expand the expression. Use the Laws of Logarithms to expand the expression. log(10^x/x(x^2+5)(x^7+6)) thanks for your help!      Log On


   

Question 198949: Hello!
Use the Laws of Logarithms to expand the expression.
Use the Laws of Logarithms to expand the expression.
log(10^x/x(x^2+5)(x^7+6))
thanks for your help!
Found 2 solutions by jim_thompson5910, josmiceli:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Is the expression log%2810%2C%28x%2F%28x%28x%5E2%2B5%29%28x%5E7%2B6%29%29%29%29 ????



log%2810%2C%28x%2F%28x%28x%5E2%2B5%29%28x%5E7%2B6%29%29%29%29 Start with the given expression.


log%2810%2C%28x%29%29-+log%2810%2C%28x%28x%5E2%2B5%29%28x%5E7%2B6%29%29%29 Break up the log using the identity log%28b%2C%28A%2FB%29%29=log%28b%2C%28A%29%29-log%28b%2C%28B%29%29


Break up the second log using the identity log%28b%2C%28A%2AB%29%29=log%28b%2C%28A%29%29%2Blog%28b%2C%28B%29%29


Distribute


-log%2810%2C%28x%5E2%2B5%29%29-log%2810%2C%28x%5E7%2B6%29%29 Combine like terms.


So

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
log%2810%5Ex%2Fx%28x%5E2%2B5%29%28x%5E7%2B6%29%29
The 1st rule I will use is:
log%28a%2Fb%29+=+log%28a%29+-+log%28b%29

The next rule is:
log%28a%5Eb%29+=+b%2Alog%28a%29

The next rule is :
log%28a%2Ab%2Ac%29+=+log%28a%29+%2B+log%28b%29+%2B+log%28c%29

Another rule is:
log%2810%29+=+1
answer