JEE MainMathematicsToughLogarithm

Equation $\log_{4}(2x^{2} + x + 1) - \log_{2}(2x - 1) = 1$ has

Show answer and solution

\log_{4}(2x^{2} + x + 1) - \log_{2}(2x - 1) = 1

Domain (i)

\ 2x^{2} + x + 1 > 0 \Rightarrow x \in R

(ii)

2x - 1 > 0 \Rightarrow x > \frac{1}{2}

.....(1)

\frac{\sqrt{2x^{2} + x + 1}}{2x - 1} = 2 \Rightarrow x = 1,\frac{3}{14}

.....(2)
(1) & (2), x = 1

Source: Grass-G / M-16 Mathematics Paper 25 Nov First.docx

Need a video for this idea?

Scan any doubt from your notes and get a whiteboard explanation.