Question

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a) \(log_2\dfrac{1}{16}\)

b) \(log_3243\)

c) \(9^{log_37}\)

d) \(\left(\dfrac{1}{81}\right)^{log_32}\)

Answer 1

a: \(log_2\dfrac{1}{16}=log_22^{-4}=-4\)

b: \(log_3243=log_33^5=5\)

c: \(9^{log_37}=7^{log_39}=7^2=49\)

c: \(\left(\dfrac{1}{81}\right)^{log_32}=\left(3^{-4}\right)^{log_32}=2^{log_33^{-4}}=2^{-4}=\dfrac{1}{16}\)

Answer 2

\(log_2\dfrac{1}{16}=-log_22^4=-4\)

\(log_3243=log_33^5=5\)

\(9^{log_37}=3^{2log_37}=3^{log_349}=49\)

\(\left(\dfrac{1}{81}\right)^{log_32}=3^{-4.log_32}=3^{log_32^{-4}}=2^{-4}=\dfrac{1}{16}\)