Show that ${log}_{b} a {log}_{c} b {log}_{a} c = 1$

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Solution

L.H.S $= {log}_{b} a {log}_{c} b {log}_{a} c$

$= \frac{log a}{log b} \times \frac{log b}{log c} \times \frac{log c}{log a}$

$= 1$

$=$ R.H.S

Hence proved.

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