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Official 2022 Paper 2 · Q15

Paper 2Logic & proofPowers & logarithms

The real numbers xx, yy and zz are all greater than 1, and satisfy the equations

log⁡xy=zandlog⁡yz=x.\log_xy=z\quad\text{and}\quad\log_yz=x.

Which one of the following equations for log⁡zx\log_zx must be true?

Alog⁡zx=y\log_zx=y
Blog⁡zx=1y\log_zx=\frac1y
Clog⁡zx=xy\log_zx=xy
Dlog⁡zx=1xy\log_zx=\frac1{xy}
Elog⁡zx=xz\log_zx=xz
Flog⁡zx=1xz\log_zx=\frac1{xz}
Glog⁡zx=yz\log_zx=yz
Hlog⁡zx=1yz\log_zx=\frac1{yz}

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