Question

solve log base 2x-1 of ( x^4+2)/(2x+1) = 1

Answer 1

Given :   log base 2x-1 of ( x^4+2)/(2x+1) = 1    $log_{2x-1} \frac{x^4 + 2}{2x+1} = 1$

To find : Value of x

Solution:

log base 2x-1 of ( x^4+2)/(2x+1) = 1

$log_{2x-1} \frac{x^4 + 2}{2x+1} = 1$

=> (2x - 1)¹  =    (x⁴ + 2)/(2x + 1)

=> 4x²  - 1 = x⁴  + 2

=> x⁴  - 4x²  + 3 = 0

=> x⁴ - x² - 3x² + 3 = 0

=> x²(x² - 1) - 3(x² - 1) = 0

=> (x² - 3)(x² - 1)  = 0

=> x² = 3   or x² = 1

=> x = ±√3  or  x = ±1

x = - 1   2x - 1 = -3 (not possible)

x = 1  2x - 1 = 1  ( there is no meaning od base to be 1 )

x = -√3   2x - 1  = -2√3 - 1  ( -ve base not possible)

x = √3    base = 2√3 - 1  

x = √3     is the Solution

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