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Simplify the following logarithms, evaluate if possible. a) log25-3 b) log3000 - log...
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Simplify/Evaluate `log_2 5^(-3)`
One of the rules of logarithm is as follows:
`log_a b^x = x log_a b`
Hence, we can simplify the given expression to:
`-3log_2 5` or `3 log_2 (1/5)`
This cannot be simplified further, but evaluating using a calculator results to: -6.97
`log3000 - log30`
We can express 3000 as `30*100`
Hence, `log3000 = log(30*100) = log30 + log100`
At this point, the expression we want to simplify is:
`log30 + log100 - log30`
`log30` simply cancels out leaving us with:
`log100 = log10^2 = 2log10 = 2`
(Here, since the base is not written, that means that the base of the operation is 10)
Posted by mvcdc on July 19, 2013 at 1:05 PM (Answer #2)
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