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Question

Part 1
Rewrite the expression ln StartFraction 5 x minus 2 Over x plus 6 EndFraction
as a​ sum, difference, or product of​ logarithms, and simplify if possible.
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Part 1
ln StartFraction 5 x minus 2 Over x plus 6 EndFraction
equals
  
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Answer 1

To rewrite the expression \( \ln \left( \frac{5x - 2}{x + 6} \right) \) as a sum or difference of logarithms, we can use the property of logarithms that states:

\[ \ln \left( \frac{a}{b} \right) = \ln(a) - \ln(b) \]

Applying this property to your expression gives:

\[ \ln \left( \frac{5x - 2}{x + 6} \right) = \ln(5x - 2) - \ln(x + 6) \]

Thus, the simplified expression is:

\[ \ln(5x - 2) - \ln(x + 6) \]