Question

Expand log 243/125
Plz tell the answers

Answer 1

Correct Question :-

Expand $\log \frac{343}{125}$

Solution :-

Expanding

$\rm:\longmapsto{ log \bigg( \frac{343}{125} \bigg) } \\ \\ \rm:\longmapsto{ log \bigg( \frac{7 {}^{3} }{5 {}^{3} } \bigg) } \\ \\ \rm:\longmapsto{ log \bigg( \frac{7}{5} \bigg) {}^{3} }$

We know that,

$\rm:\longmapsto{ log \: a {}^{n} = n \: log \:a }$

Now,

$\rm:\longmapsto{3 \: log \bigg( \frac{7}{5} \bigg) }$

We also know that,

$\rm:\longmapsto{log \bigg( \frac{x}{y} \bigg) = log \: x - log \: y }$

Then,

$\rm:\longmapsto{3 \: log \: 7 - 3 log \: 5 } \\ \\ \rm{or} \\ \\ \rm:\longmapsto{ 3( log \: 7 - log \: 5) }$

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