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Chapter 13: Problem 47

Write as the sum or difference of logarithms and simplify, if possible. Assume all variables represent positive real numbers. $$\log k(k-6)$$

Short Answer

Expert verified
The short version of the answer is: \( \log k(k-6) = \log k + \log (k-6). \)

Step by step solution

01

Apply the product rule of logarithms

The given function is \( \log k(k-6) \). To rewrite the product inside the logarithm as a sum of logarithms, we will use the product rule of logarithms, which states that: \[ \log (ab) = \log a + \log b \] So, the expression becomes: \[ \log k(k-6) = \log k + \log (k-6).\]
02

Simplify if possible and write the final expression

In this case, we cannot further simplify the expression, as there are no other properties of logarithms that can be applied. Therefore, the final expression is: \[ \log k(k-6) = \log k + \log (k-6). \] This is the given expression written as the sum of two logarithms.

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Most popular questions from this chapter

Write as a single logarithm. Assume the variables are defined so that the variable expressions are positive and so that the bases are positive real numbers not equal to \(1 .\) $$\log _{7} 8-4 \log _{7} x-\log _{7} y$$

Given that \(\log 5=0.6990\) and \(\log 9=0.9542,\) use the propertics of logarithms to approximate the following $$\log 45$$

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