Question

log 14/15-log 3/25-log7/9 value of​

Answer 1

Answer:

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

Step-by-step explanation:

Formula used:

Product rule:

$log_a(MN)=log_aM+log_aN$

Quotient rule:

$log_a(\frac{M}{N})=log_aM-log_aN$

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

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

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

$=log\frac{14}{15}-log(\frac{1}{25}*\frac{7}{3})$ ​

$=log\frac{14}{15}-log\frac{7}{75}$ ​

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

$=log(\frac{14}{15}*\frac{75}{7})$ ​

$=log(2*5)$ ​

$=log_{10}10$ if we consider the base as 10

$=1$

Answer 2

Answer ⇒  log10 or 1

Explanation ⇒  We will use the formula,

loga/b = log a - log b

Thus, log14/15 - log3/25 - log7/9

= log14 - log15 - log3 + log25 - log7 + log9

= log(7 × 2) - log(3 × 5) - log3 + log(5 × 5) - log7 + log(3 × 3)

= log7 + log2 - log3 - log3 - log5 + log5 + log5 - log7 + log3 + log3

[Since, log(a × b) = loga + logb]

= log2 + log5

= log(2 × 5)

= log10  

= 1

Hence, the value of the given expression is log10 or 1.

Hope it helps.