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Logarithmic Radius and Circumference

Source: AMC 12 2008B Problem 14

February 29, 2008
logarithmsAMC

Problem Statement

A circle has a radius of log⁡10(a2) \log_{10}(a^2) and a circumference of log⁡10(b4) \log_{10}(b^4). What is log⁡ab \log_ab? <spanclass=′latex−bold′>(A)</span> 14π<spanclass=′latex−bold′>(B)</span> 1π<spanclass=′latex−bold′>(C)</span> π<spanclass=′latex−bold′>(D)</span> 2π<spanclass=′latex−bold′>(E)</span> 102π <span class='latex-bold'>(A)</span>\ \frac {1}{4\pi} \qquad <span class='latex-bold'>(B)</span>\ \frac {1}{\pi} \qquad <span class='latex-bold'>(C)</span>\ \pi \qquad <span class='latex-bold'>(D)</span>\ 2\pi \qquad <span class='latex-bold'>(E)</span>\ 10^{2\pi}
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