Question

Ch
Q.2. Find the value :
log (x + 1) + log (x - 1) = log 3
​

Answer 1

Answer:

3log2+log3=log (2^3)+log(3)

=log8 + log3

=log(8*3)

= log24

Answer 2

Step-by-step explanation:

Given:-

log (x + 1) + log (x - 1) = log 3

To find:-

Find the value of x in log (x+1)+log (x-1) = log 3

Solution:-

Given that:-

log (x + 1) + log (x - 1) = log 3

we know that

log a + log b = log (ab)

=>log (x+1)(x-1) = log 3

(x+1)(x-1) is in the form of (a+b)(a-b).

Here a = x and b= 1

(a+b)(a-b) = a^2-b^2

(x+1)(x-1)=x^2-1

=>log (x^2-1) = log 3

Therefore, x^2-1 = 3

=>x^2 = 3+1

=>x^2 = 4

=>x=±√4

=>x= ±2

Therefore , x = 2 and -2

Answer:-

The value of x in log (x + 1) + log (x - 1) = log 3 is

2 and -2

Check:-

(i)If x= 2 then LHS

log(x+1)+log(x-1)

=>log(2+1)+log(2-1)

=>log 3 +log 1

=>log (3×1)

=>log 3

=>RHS

LHS=RHS

(ii)if x= -2 the LHS

log(x+1)+log(x-1)

=>log(-2+1)+log(-2-1)

=>log(-1)+(log(-3)

=>log(-1×-3)

=>log 3

=>RHS

LHS = RHS is true for x= 2 and -2

Used formula:-

• log a + log b = log ab