If \(\log_{3}a - 2 = 3\log_{3}b\), express a in terms of b.
Question 1 Report
If \(\log_{3}a - 2 = 3\log_{3}b\), express a in terms of b.
Answer Details
The given equation is \(\log_{3}a - 2 = 3\log_{3}b\). We can use the logarithmic property that \(\log_{a}b^{c} = c\log_{a}b\) to simplify the equation:
\(\log_{3}a - 2 = \log_{3}b^{3}\)
\(\log_{3}a = \log_{3}b^{3} + 2\)
\(\log_{3}a = \log_{3}(b^{3}\cdot 3^{2})\)
Using the property that if \(\log_{a}b = \log_{a}c\) then \(b = c\), we get:
\(a = b^{3}\cdot 3^{2}\)
\(a = 9b^{3}\)
Therefore, the value of \(a\) in terms of \(b\) is \(a = 9b^{3}\).
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