Choose-the-correct-option-If-a-b-and-c-are-consecutive-positive-integers-and-log-1-ac-2k-then-the-value-of-k-is-a-log-a-b-log-b-c-2-d-1-Give-the-explaination-also-

Question Number 193230 by MATHEMATICSAM last updated on 07/Jun/23

Choose the correct option :

If a, b and c are consecutive positive

integers and \log (1 + a c) = 2 k then the

value of k is :

a) \log a

b) \log b

c) 2

d) 1

Give the explaination also .

Answered by Rajpurohith last updated on 08/Jun/23

l e t a = b - 1; c = b + 1 (s i n c e a, b a n d c a r e c o n s e c u t i v e .)

s o 1 + a c = 1 + (b - 1) (b + 1) = 1 + b^{2} - 1 = b^{2}

\Rightarrow l o g (1 + a c) = l o g (b^{2}) = 2 l o g (b) = 2 k

h e n c e k = l o g (b) .