Question

If logx (8x-3) -logx 4=2, the value of x is

Answer 1

Answer:

x = 1/2 and 3/2

Step-by-step explanation:

The given equation is logₓ (8x-3) - logₓ 4 = 2

Then we have to determine the value of x.

logₓ $[\frac{(8x-3)}{4}]$ = 2    [ since log a - log b = log $(\frac{a}{b})$ ]

Now $x^{2}=\frac{(8x-3)}{4}$   [if $log_{a}$b = c then $a^{c}$ = b]

4x² = 8x -3

4x² - 8x + 3 = 0

(2x)² - 2(4x) + (4-4) + 3 = 0

[(2x)² - 2 (4x) + 4 ] - 1 = 0

(2x - 2)² = 1

(2x - 2)² = ± 1 ⇒

2x - 2 = 1       and      2x - 2 = -1

x = 3/2                        2x = 1

                                    x = 1/2

Therefore, x = 1/2 and 3/2 are the answers.