Solve for x : log (x - 1) + log (x + 1) = log 2 1

Given, ⇒ log (x - 1) + log (x + 1) = log 2 1 ⇒ log (x - 1)(x + 1) = 0 ⇒ log (x 2 + x - x - 1) = 0 ⇒ log (x 2 - 1) = 0 ⇒ x 2 - 1 = 10 0 ⇒ x 2 - 1 = 1 ⇒ x 2 = 1 + 1 ⇒ x 2 = 2 ⇒ x = . Hence, x = .

Mathematics

Solve for x :
log (x - 1) + log (x + 1) = log₂ 1

Logarithms

3 Likes

Answer

Given,

⇒ log (x - 1) + log (x + 1) = log₂ 1

⇒ log (x - 1)(x + 1) = 0

⇒ log (x² + x - x - 1) = 0

⇒ log (x² - 1) = 0

⇒ x² - 1 = 10⁰

⇒ x² - 1 = 1

⇒ x² = 1 + 1

⇒ x² = 2

⇒ x = $\sqrt{2}$ .

Hence, x = $\sqrt{2}$ .

Answered By

3 Likes

Related Questions

Assertion (A): log 2 = a and log 3 = b
⇒ 1 + log 12 = 2a + b
Reason (R): 1 + log 12
= 1 + log 2 x 2 x 3
= 1 + 2log 2 + log 3
= 1 + 2a + b
A is true, but R is false.
A is false, but R is true.
Both A and R are true and R is the correct reason for A.
Both A and R are true and R is the incorrect reason for A.
View Answer

If log₂ x = a and log₃ y = a, write 72^a in terms of x and y.
View Answer
If log (x² - 21) = 2, show that x = $\pm 11$ .
View Answer
If x = (100)^a, y = (10000)^b and z = (10)^c, find log $\dfrac{10\sqrt{y}}{x^2z^3}$ in terms of a, b and c.
View Answer

Mathematics

Solve for x :log (x - 1) + log (x + 1) = log2 1

Logarithms

Answer

Related Questions

If log2 x = a and log3 y = a, write 72a in terms of x and y.

If log (x2 - 21) = 2, show that x = ±11\pm 11±11.

If x = (100)a, y = (10000)b and z = (10)c, find log 10yx2z3\dfrac{10\sqrt{y}}{x^2z^3}x2z310y​​ in terms of a, b and c.

Solve for x :
log (x - 1) + log (x + 1) = log₂ 1

If log₂ x = a and log₃ y = a, write 72^a in terms of x and y.

If log (x² - 21) = 2, show that x = $\pm 11$ .

If x = (100)^a, y = (10000)^b and z = (10)^c, find log $\dfrac{10\sqrt{y}}{x^2z^3}$ in terms of a, b and c.