Discussion

Explanation:

log₅17 × log₁₇19 × log₁₉56 × log₅₆125 = ?

Here we can use property of logarithm, log_ba = $\frac{{\log }_{\mathrm{m}}\mathrm{a}}{{\log }_{\mathrm{m}}\mathrm{b}}$

Hence, converting all logs in base 10 i.e., taking m = 10 for all logs, we get

Given expression = $\frac{{\log }_{10}17}{{\log }_{10}5}$ × $\frac{{\log }_{10}19}{{\log }_{10}17}$ × $\frac{{\log }_{10}56}{{\log }_{10}19}$ × $\frac{{\log }_{10}125}{{\log }_{10}56}$

log₁₀17, log₁₀19, log₁₀56 cancels out, we get

Given, expression = $\frac{{\log }_{10}125}{{\log }_{10}5}$ = log₅125 = log₅5³ = 3log₅125 = 3

Hence, option (b).

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