1.

If log (x - 9) + log x= 1, then x=​

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SOLUTION :-

⇒ log (x - 9) * x = 1

[ Because log a + log B = log AB ]

⇒ log (x² - 9x) = 1

⇒ log (x² - 9x) = 1

Here we will assume the base as 10

⇒ log₁₀ (x² - 9x) = 1

⇒ log₁₀ (x² - 9x) = log₁₀ 10

[ Because 1 = logₓ x = 1 ]

Eliminating log on both sides

⇒ x² - 9x = 10

⇒ x² - 9x - 10 = 0

Splitting the middle term

⇒ x² - 10x + x - 10 = 0

⇒ x(x - 10) + 1(x - 10) = 0

⇒ (x + 1)(x - 10) = 0

⇒ x + 1 = 0 or x - 10 = 0

⇒ x = - 1 or x = 10

x ≠ - 1 since log of negative value is undefined

⇒ x = 10

Therefore the value of x is 10.


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