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1 of 8 0-day streak

Express one logarithmic quantity in terms of another

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Question 1 of 8

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Let \(r=\log_{3}\left(t\right)\). The variable \(t\) is positive. The base \(3\) and every displayed logarithm base are positive and are not 1

\[-9\log_{\left(3\right)^{3}}\left(\left(3\right)\,t^{-2}\right)\]

The displayed relation may be used in either logarithmic or exponential form

(a)1 mark

Which form gives the displayed quantity using \(r\)?

(b)3 marks

Complete the table with the exact numerical coefficients and argument exponents

\[-9\log_{\left(3\right)^{3}}\left(\left(3\right)\,t^{-2}\right)\]