SOLUTION: Express as an equivalent expression that is a sum of logarithms thanks log t (3ab) the t should be a little lower than the g in log. thanks

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Question 248665: Express as an equivalent expression that is a sum of logarithms thanks
log t (3ab) the t should be a little lower than the g in log. thanks
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
log%28t%2C%283ab%29%29 Start with the given expression


log%28t%2C%283a%29%29%2Blog%28t%2C%28b%29%29 Break up the log using the identity log%28c%2C%28xy%29%29=log%28c%2C%28x%29%29%2Blog%28c%2C%28y%29%29.

Note: Using the identity, this means that x=3a and y=b


log%28t%2C%283%29%29%2Blog%28t%2C%28a%29%29%2Blog%28t%2C%28b%29%29 Break up the first log using the identity log%28c%2C%28xy%29%29=log%28c%2C%28x%29%29%2Blog%28c%2C%28y%29%29 again.

Note: Using the identity, this means that x=3 and y=a


So log%28t%2C%283ab%29%29=log%28t%2C%283%29%29%2Blog%28t%2C%28a%29%29%2Blog%28t%2C%28b%29%29


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As you can see (or if you do more examples, you will see), the log of the product of any number of factors is simply the sum of the logs of those factors. In other words, this idea generalizes for any number of terms being multiplied.

So for example,