SOLUTION: Write the following using a single logarithm. 1/3log a - 3log b + 8log c + 6log b

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Question 487298: Write the following using a single logarithm.
1/3log a - 3log b + 8log c + 6log b
Answer by mervh1967(6) About Me  (Show Source):
You can put this solution on YOUR website!
Use the basic properties of logarithms:
Remember n%2Alog%28x%29=log%28x%5En%29
so we can write the expression as:
log%28a%5E%281%2F3%29%29-log%28b%5E3%29%2Blog%28c%5E8%29%2Blog%28b%5E6%29
Now, another property of logs states:
log%28x%29%2Blog%28y%29=log%28x%2Ay%29 and
log%28x%29-log%28y%29=log%28x%2Fy%29
so the equation becomes:
log%28a%5E%281%2F3%29%2Ac%5E8%2Ab%5E6%2Fb%5E3%29=log%28a%5E%281%2F3%29%2Ac%5E8%2Ab%5E3%29
merv