The number of solution(s) of ${log}_{2} | 1 - x | = 2 {log}_{2} | x - 3 |$ is

Open in App

Solution

${log}_{2} | 1 - x | = 2 {log}_{2} | x - 3 |$
$\Rightarrow {log}_{2} | 1 - x | = {log}_{2} (x - 3)^{2}$
$\Rightarrow {log}_{2} \frac{| 1 - x |}{(x - 3)^{2}} = 0$
$\Rightarrow \frac{| 1 - x |}{(x - 3)^{2}} = 1$
$\Rightarrow | 1 - x | = (x - 3)^{2}$

Clearly, there are two solutions.

Suggest Corrections

Similar questions

2 {log}_{2} {log}_{2} x + {log}_{1 / 2} {log}_{2} (2 \sqrt{2} x) = 1

{log}_{4} (x - 1) = {log}_{2} (x - 3)

{log}_{2} x + \frac{1}{2} {log}_{2} (x + 2) = 2

2 {log}_{2} ({log}_{2} x) + {log}_{\frac{1}{2}} ({log}_{2} 2 \sqrt{2} x) = 1

x

2 {log}_{2} \frac{x - 7}{x - 1} + {log}_{2} \frac{x - 1}{x + 1} = 1

Join BYJU'S Learning Program