Question

The number of solution of $\log_{4}(x - 1) = \log_{2}(x - 3)$

• A. 3
• B. 1
• C. 2
• D. 0

Answer 1

Answer: (B)

1

Answer 2

We have $\log_{4}(x - 1) = \log_{2}(x - 3)$

$(x - 1) = (x - 3)^{2}$ ⇒ $x - 1 = x^{2} + 9 - 6x$ ⇒ $x^{2} - 7x + 10 = 0$

⇒ $(x - 5)(x - 2) = 0$

$x = 5$ or $x = 2$

But $x - 3 < 0$, when $x = 2$. ∴ Only solution is $x = 5$.

Hence number of solution is one.