MathDB

13

Part of 2020 AMC 12/AHSME

Problems(2)

Nested Roots

Source: 2020 AMC 12A #13

1/31/2020
There are integers aa, bb, and cc, each greater than 1, such that NNNca=N2536\sqrt[a]{N \sqrt{N \sqrt[c]{N}}} = \sqrt[36]{N^{25}} for all N>1N > 1. What is bb?
<spanclass=′latex−bold′>(A)</span> 2<spanclass=′latex−bold′>(B)</span> 3<spanclass=′latex−bold′>(C)</span> 4<spanclass=′latex−bold′>(D)</span> 5<spanclass=′latex−bold′>(E)</span> 6<span class='latex-bold'>(A)</span>\ 2\qquad<span class='latex-bold'>(B)</span>\ 3\qquad<span class='latex-bold'>(C)</span>\ 4\qquad<span class='latex-bold'>(D)</span>\ 5\qquad<span class='latex-bold'>(E)</span>\ 6
2020 AMC 12A2020 AMCAMC 12AMC 12 AAMC
Tricky Logarithms

Source: 2020 AMC 12B #13

2/6/2020
Which of the following is the value of log⁡26+log⁡36?\sqrt{\log_2{6}+\log_3{6}}?
<spanclass=′latex−bold′>(A)</span>1<spanclass=′latex−bold′>(B)</span>log⁡56<spanclass=′latex−bold′>(C)</span>2<spanclass=′latex−bold′>(D)</span>log⁡23+log⁡32<spanclass=′latex−bold′>(E)</span>log⁡26+log⁡36<span class='latex-bold'>(A) </span> 1 \qquad<span class='latex-bold'>(B) </span> \sqrt{\log_5{6}} \qquad<span class='latex-bold'>(C) </span> 2 \qquad<span class='latex-bold'>(D) </span> \sqrt{\log_2{3}}+\sqrt{\log_3{2}} \qquad<span class='latex-bold'>(E) </span> \sqrt{\log_2{6}}+\sqrt{\log_3{6}}
AMC 12 BAMCAMC 12logarithms2020 AMC 12B2020 AMC