Evaluate; \(\frac{\log_3 9 - \log_2 8}{\log_3 9}\)
Question 1 Report
Evaluate; \(\frac{\log_3 9 - \log_2 8}{\log_3 9}\)
Answer Details
We can use the laws of logarithms to simplify the expression:
\(\frac{\log_3 9 - \log_2 8}{\log_3 9} = \frac{\log_3 (3^2) - \log_2 (2^3)}{\log_3 (3^2)}\)
Using the laws of logarithms, we can simplify the numerator:
\(\frac{\log_3 (3^2) - \log_2 (2^3)}{\log_3 (3^2)} = \frac{2\log_3 3 - 3\log_2 2}{2\log_3 3}\)
We know that \(\log_3 3 = 1\) and \(\log_2 2 = 1\), so we can substitute these values:
\(\frac{2\log_3 3 - 3\log_2 2}{2\log_3 3} = \frac{2 - 3}{2} = -\frac{1}{2}\)
Therefore, the value of the expression is -\(\frac{1}{2}\).
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