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Official 2016 Paper 1 · Q16

Paper 1Powers & logarithmsAlgebra

Given the simultaneous equations

log⁡102+log⁡10(y−1)=2log⁡10xlog⁡10(y+3−3x)=0\begin{aligned} \log_{10}2+\log_{10}(y-1)&=2\log_{10}x\\ \log_{10}(y+3-3x)&=0 \end{aligned}

the values of yy are

A52±352\dfrac{5}{2}\pm\dfrac{3\sqrt{5}}{2}
B3±33\pm\sqrt{3}
C7±337\pm3\sqrt{3}
D3,93,9
E1,131,13

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