# How do you solve #log_2((-9x)/(2x^2-1)) = 1# ?

##### 1 Answer

May 30, 2016

#### Explanation:

#log_2((-9x)/(2x^2-1)) = log_2(-9x)-log_2(2x^2-1) = 1 = log_2 2#

Since

#(-9x)/(2x^2-1) = 2#

Multiplying both sides by

#-9x = 4x^2-2#

Add

#4x^2+9x-2 = 0#

Use the quadratic formula to find roots:

#x = (-9+-sqrt(9^2-(4*4*-2)))/(2*4)#

#=(-9+-sqrt(81+32))/8#

#=(-9+-sqrt(123))/8#

We can discard

That leaves