Here, the given equation is ln(4x−2)−ln4=−ln(x−2)ln?(4x−2)−ln?4=−ln?(x−2). We have to find the value of xx.

∴ln(4x−2)−ln4=−ln(x−2)ln(4)−ln(4x−2)=ln(x−2)ln44x−2=ln(x−2)[ lna−lnb=lnab ]Now, removing loge (ln) from both sides.44x−2=x−24=(4x−2)(x−2)4=4x2−8x−2x+44x2−10x+4−4=04x2−10x=02x(2x−5)=0∴x=0 [or] 2x−5=02x=5x=52∴ln?(4x−2)−ln?4=−ln?(x−2)ln?(4)−ln?(4x−2)=ln?(x−2)ln?44x−2=ln?(x−2)[ ln?a−ln?b=ln?ab ]Now, removing loge? (ln) from both sides.44x−2=x−24=(4x−2)(x−2)4=4x2−8x−2x+44x2−10x+4−4=04x2−10x=02x(2x−5)=0∴x=0 [or] 2x−5=02x=5x=52

Therefore, x=0, 52x=0, 52.