Number of value(s) of x satisfying the equation ln(1+x) =ln(1+x)+ (1+x)^(2) -3 is (where . represents greatest integer function)​

Move all the terms containing a logarithm to the left side of the equation. ln ( 1 + x ) − ln ( 1 + x ) = ( 1 + x ) 2 − 3 USE the QUOTIENT property of logarithms, log b ( x ) − log b ( y ) = log b ( x y ) . ln ( 1 + x 1 + x ) = ( 1 + x ) 2 − 3 Cancel the common factor of 1 + x . Tap for more steps... ln ( 1 ) = ( 1 + x ) 2 − 3 The natural logarithm of 1 is 0 . 0 = ( 1 + x ) 2 − 3 SIMPLIFY ( 1 + x ) 2 − 3 . Tap for more steps... 0 = 2 x + x 2 − 2 Since x is on the right side of the equation, SWITCH the sides so it is on the left side of the equation. 2 x + x 2 − 2 = 0 Use the quadratic formula to find the solutions. − b ± √ b 2 − 4 ( a C ) 2 a Substitute the values a = 1 , b = 2 , and c = − 2 into the quadratic formula and solve for x . − 2 ± √ 2 2 − 4 ⋅ ( 1 ⋅ − 2 ) 2 ⋅ 1 Simplify. Tap for more steps... x = − 1 ± √ 3 The final answer is the combination of both solutions. x = − 1 + √ 3 , − 1 − √ 3 Exclude the solutions that do not make ln ( 1 + x ) = ln ( 1 + x ) + ( 1 + x ) 2 − 3 true. x = − 1 + √ 3 The result can be shown in multiple forms. Exact Form: x = − 1 + √ 3 Decimal Form: x = 0.73205080 …