Question

log (2x-3)+log (x+1)=2log5 what is the value of x

Answer 1

Please see the attachment

Answer 2

Given,

$log(2x - 3) + log(x + 1) = 2 log(5)$

To find,

The value of x.

Solution,

The value of x will be 4 or -7/2.

We can easily solve this problem by following the given steps.

According to the question,

$log(2x - 3) + log(x + 1) = 2 log(5)$

We know that (log m) + (log n) = log (mn).

Now, using this for the expression on the left hand side,

$log (2x-3)(x+1) = 2 log(5)$

$log (2x²+2x-3x-3) = 2 log(5)$

$log (2x²-x-3) = 2 log(5)$

We know:

n log m = log mⁿ

Now, using this for the expression on the right-hand side,

$log (2x²-x-3) = log (5)²$

We know that if log m = log n then m = n.

So,

(2x²-x-3) = 25

2x²-x-3-25 = 0

2x²-x-28 = 0

Now, factorising this by splitting the middle term such that their subtraction is -x and multiplication is (-28×2x²),

2x²-8x+7x-28 = 0

2x(x-4)+7(x-4) = 0

(x-4)(2x+7) = 0

Equating both the brackets with 0,

(x-4) = 0 or (2x+7) = 0

x = 4 or x = -7/2

Hence, the value of x is 4 or -7/2.