Question

if loga+logb = loga-logb then find a&​

Answer 1

Identities Used:

$log \:a + log \:b = log\:ab\\log \:a - log \:b = log\:\frac{a}{b}$

To find:

a = ?

b = ?

Given that:

log a + log b = log a-log b

Applying the Identities:

=>$log\:a + log\:b = log\:a - log\:b$

=>$log\:ab = log\:\frac{a}{b}$

=> Now, applying antilog, we get,

=> $ab = \frac{a}{b}$

=> dividing both sides by a, we get,

=> $b = \frac{1}{b}$

=>$b^{2} = 1$ (Taking square root on both sides) .

=> b = 1

=> Substituting this value in