SOLUTION: Logb (√b^7/b^4) = ?

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Logb (√b^7/b^4) = ?       Log On


   

Question 709742: Logb (√b^7/b^4) = ?

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
What is inside the square root? Just the b%5E7 or the whole fraction b%5E7%2Fb%5E4? Please put parentheses around radicands (the expression within a radical is called a radicand) so we can see what is inside a square root.

Without knowing what is in the square root I cannot answer the question. But I can give you some guidance:
  1. Change the square root to a power of 1/2. For example: sqrt%28b%5E7%29+=+%28b%5E7%29%5E%281%2F2%29
  2. Use your rules for exponents to simplify the expression down to "b" to some power. At this point you may already know what the answer is. If not...
  3. Use the log%28a%2C+%28p%5En%29%29+=+n%2Alog%28a%2C+%28p%29%29 property of logarithms to move the exponent of b out in front of the log. For example:
    log%28b%2C+%28b%5E%287%2F5%29%29%29+=+%287%2F5%29%2Alog%28b%2C+%28b%29%29
  4. You now have some number times log%28b%2C+%28b%29%29. You should that any log where the base and the argument are the same is equal to 1. So the whole expression simplifies to just the number in front. For example:
    %287%2F5%29%2Alog%28b%2C+%28b%29%29+=+%287%2F5%29%2A1+=+7%2F5