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Which of the following is true ?

1. $\log_{17} 275 = \log_{19} 375$
2. $\log_{17} 275 > \log_{19} 375$
3. $\log_{17} 275 < \log_{19} 375$
4. None of these

option C
how ?

let,

$\log_{17}275 =x$

so,$17^{x}=275$              …………….(1)

$\log_{19}375=y$

so,$19^{y}=375$               …………………...(2)

(1)$\div$(2)

$\frac{17^{x}}{19^{y}}=\frac{275}{375}< 1$

so,$17^{x}<19 ^{y}$

taking log both sides respect to base 19,

$x*\log_{19}17< y$

so, $\frac{x}{y}< 1$ ………..[as $\log_{17}19 > 1$]

so,$x< y$

[note ,

$\log_{17}275=1.984$

$\log_{19}375=2.012$

if you are allowed to use calculator which i believe you are not]