Question

Write each logarithmic expression as one logarithm. See Example 7. $$ \log _{3} x+\log _{3}(x+2)-\log _{3} 8 $$

          Write each logarithmic expression as one logarithm. See Example 7.
$$
\log _{3} x+\log _{3}(x+2)-\log _{3} 8
$$

Added by Robert M.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

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Solved by Expert Maria Dearborn

Step 1

So, we have: $$ \log_3{x} + \log_3{(x+2)} = \log_3{x(x+2)} = \log_3{x^2+2x} $$ Now, we can combine this with the third logarithm using the quotient rule: $\log_a{m} - \log_a{n} = \log_a{\frac{m}{n}}$. Show more…

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Write each logarithmic expression as one logarithm. See Example 7. $$ \log _{3} x+\log _{3}(x+2)-\log _{3} 8 $$

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Write each logarithmic expression as one logarithm. See Example 7. $$ \log _{3} x+\log _{3}(x+2)-\log _{3} 8 $$

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