Question

log14/15 - log3/25 - log7/9 =?? ?​

Answer 1

Answer:

1

Step-by-step explanation:

$log \frac{14}{15}-log \frac{3}{25}-log \frac{7}{9}$

$=log \frac{14}{15}-(log \frac{3}{25}+log \frac{7}{9})$

$=log \frac{14}{15}-log (\frac{3}{25}\times \frac{7}{9})$

/* log m + log n = log mn*/

$=log\frac{14}{15}-log\frac{7}{75}$

$= log \left(\frac{\frac{14}{15}}{\frac{7}{75}}\right)$

$Since, \boxed {log m - log n = log \frac{m}{n}}$

$= log \left(\frac{14}{15}\times \frac{75}{7}\right)$

$=log (2\times 5)\\=log 10\\=log_{10}10= 1$

Therefore,

$log \frac{14}{15}-log \frac{3}{25}-log \frac{7}{9}=1$

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