Question

if log 21=1.322 and log 3=0.04771 find log 7​

Answer 1

Given

log 21 = 1.322

log 3 = 0.04771

To Find

Value of log 7

Solution

By the identity

$\boxed{log</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>a </strong><strong>+</strong><strong> </strong><strong>log</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>b</strong><strong> </strong><strong>=</strong><strong> </strong><strong>log</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>ab</strong><strong>}$

we can write,

log 21 = log (3)(7)

log 21 = log 3 + log 7

put the values

1.322 = 0.04771 + log 7

log 7 = 1.322 - 0.04771

$\boxed{log 7 = 1.27429}$

Answer 2

Given :-

log 21 = 1.322

log 3 = 0.04771

To find :-

log 7

Solution :-

Consider log 21

log 21 can be written as log 7(3) because 21 can be written as 7(3)

⇒ log 21 = log 7(3)

⇒ log 21 = log 7 + log 3

$\\ \boxed{ \bf \because log \: ab = log \: a + log \: b}$

Here

• log 21 = 1.322

• log 3 = 0.04771

By substituting these values in the above equation

⇒ 1.322 = log 7 + 0.04771

Traspose 0.04771 to LHS

⇒ 1.322 - 0.04771 = log 7

⇒ 1.27429 = log 7

⇒ log 7 = 1.27429

Therefore log 7 = 1.27429