Question

2logx - log(x-1) = log(x-2)

Answer 1

Answer:

The final value of x is $\frac{2}{3}$

Step-by-step explanation:

For finding up the value of the given expression we first will use some log function formulas as written below:

n log x = $logx^{n}$ and also log a + log b = loga×b

2 log x - log (x-1) = log (x-2)

⇒ $logx^{2}$ - log(x-1) = log(x-2)

⇒log$x^{2}$ = log (x-2) + log (x-1)

⇒log$x^{2}$ = log (x-2)(x-1)

⇒$x^{2}$ = (x-2)(x-1)

⇒$x^{2}$ = $x^{2}$ - 3x + 2

⇒ -3x + 2 = $x^{2} -x^{2}$

⇒ -3x + 2 =0

⇒ -3x = -2

⇒ x = $\frac{-2}{-3}$

⇒ x = $\frac{2}{3}$

Therefore we find the value of x to be $\frac{2}{3}$