Evaluate log317log925-log417log523-

log _ 3 17 log _ 9 25 log _ 4 17 log _ 5 23 = log17/log3 2log5/2log3 log17/2log2 log23/log5 = log17 log5 log17.log5 log23.log4 ...

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Standard IX

Mathematics

Property 5

Evaluate lo...

Question

Evaluate $\frac{{log}_{3} 17}{{log}_{9} 25} - \frac{{log}_{4} 17}{{log}_{5} 23}$ .

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Solution

$\frac{{l o g}_{3} 17}{{l o g}_{9} 25} - \frac{{l o g}_{4} 17}{{l o g}_{5} 23}$
$= \frac{l o g 17 / l o g 3}{2 l o g 5 / 2 l o g 3} - \frac{l o g 17 / 2 l o g 2}{l o g 23 / l o g 5}$
$= \frac{l o g 17}{l o g 5} - \frac{l o g 17. l o g 5}{l o g 23. l o g 4}$
$= l o g 17. [\frac{1}{l o g 5} - \frac{l o g 5}{l o g 23 l o g 4}]$

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Evaluate log317log925−log417log523.

log317log925−log417log523=log17/log32log5/2log3−log17/2log2log23/log5=log17log5−log17.log5log23.log4=log17.[1log5−log5log23log4]

Evaluate $\frac{{log}_{3} 17}{{log}_{9} 25} - \frac{{log}_{4} 17}{{log}_{5} 23}$ .