Question

If a = log503 and c = log 5 , then the value of log2012 in terms of a and c is

Answer 1

The answer is given below :

RULE :

1. log a = b

=> a = e^b

2. log (ab)

= log a + log b

3. log (e^a) = a

SOLUTION :

Given that,

a = log 503

and

b = log 5

=> log 5 = b

=> 5 = e^b

=> 4 × 5 = 4 × e^c, multiplying both sides by 4

=> 4 = 4/5 × e^c

Taking log to both sides, we get

log 4 = log (4/5 × e^c)

=> log 4 = log (4/5) + log (e^c)

=> log 4 = log (4/5) + c

Now, log 2012

= log (503 × 4)

= log 503 + log 4

= a + log (4/5) + c

= a + c + log (4/5),
which is the required value of log (2012) in termss of a and c.

Thank you for your question.

Answer 2

HELLO DEAR,



we know that:-


1. log a = b

⇒ a = e^b

(2). log (ab)

⇒log a + log b

AND,


log (e^a) = a



Now,

Given that,

a = log 503

and

b = log 5

⇒ log 5 = b

⇒ 5 = e^b

⇒4 × 5 = 4 × e^c,
∴ [ multiply both sides by 4 ]

⇒ 4 = 4/5 × e^c
∴ [ Taking log to both sides ]


we get,



log 4 = log (4/5 × e^c)

⇒ log 4 = log (4/5) + log (e^c)


⇒ log 4 = log (4/5) + c



Now,

log 2012

⇒log (503 × 4)

⇒ log 503 + log 4

⇒ a + log (4/5) + c

= a + c + log (4/5),




HENCE,

the value of log (2012) in termss of a and c





I HOPE ITS HELP YOU DEAR,
THANKS