Question

Find the value of x.......

Answer 1

Answer:

Step-by-step explanation:

Given log (x - 3) base 3 + log(x + 2) base 3 = log 8 base 3

We know that log a + log b = log (a.b)

                 So log (x - 3)(x + 2) base 3 = log 8 base 3

        When bases are same, equating terms we get

                   (x - 3)(x + 2) = 8

               x^2 - 3 x + 2 x - 6 = 8  

              x = - b ± √b^2 - 4 ac / 2a

              x = 1 ± √1 + 56 / 2

            x = 1 + √57 / 2

Answer 2

Answer ⇒

Step-by-step explanation ⇒  

log₃ (x - 3) + log₃(x + 2) = log₃8

We know, log m + log n = log(mn)

∴ log₃[(x - 3)(x + 2)] = log₃8

On Comparing,

(x - 3)(x + 2) = 8

x² + 2x - 3x - 6 = 8

∴ x² - x - 14 = 0

On solving this quadratic equation, we will get,

x = 1 ± √(57/4)

Hope it helps.