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Evaluate the following:
9 log 3 ( 4 ) \Large 9^{\log_{3}(4)} 9log3(4)
Do not use a calculator -- not even a slide rule!
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log 2 3 × log 3 4 × log 4 5 × ⋯ × log 127 128 = ? \large \log_2 3 \times \log_3 4 \times \log_4 5 \times \cdots\times \log_{127} 128 = \, ? log23×log34×log45×⋯×log127128=?
True or false:
\quad \quad log x 1 = 0 \log_{x}1=0 logx1=0for every x > 0 x>0 x>0.
∑ cyclic ( a , b , c ) ( 1 1 + log a b c ) = ? \large \sum_{\text{cyclic}(a,b,c)} \left( \dfrac1{1 + \log_a bc} \right) = \, ? cyclic(a,b,c)∑(1+logabc1)=?
Which of the options is correct about the number log 4 18 \log _{ 4 }{ 18 } log418?
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