Question

please solve step by step explanation
given log 2 = 0.3010 log 3= 0.4771 find the value of log 25​

Answer 1

Solution :-

As we know

log(a × b) = log(a) + log(b)

log(a ÷ b) = log(a) - log(b)

Now coming back to the question :-

we can write

log(25) = log(5 × 5)

→ log(25) = log(5) + log(5)

Now as 10 ÷ 2 = 5

→ log(25) = log(10 ÷ 2) + log(10 ÷ 2)

→ log(25) = log(10) - log(2) + log(10) - log(2)

→ log(25) = 2 log(10) - 2 log(2)

→ log(25) = 2( log(10) - log(2) )

→ log(25) = 2( 1 - 0.3010)

→ log(25) = 2( 0.6990)

→ log(25) = 1.3980

So

$\huge{\boxed{\sf{log(25) = 1.398}}}$