Question

Log₃ ⁡(x²−1)=log₃ (x+1) + 1

Answer 1

Ответ:

4

Пошаговое объяснение:

log3(x^2-1)=log3(x+1)+1 ОДЗ:x^2-1>0

(x-1)(x+1)>0

lod3(x^2-1)=log3(x+1),x€(- ∞;-1)(1;+∞)

log3(x^2-1)-log(x+1)=1

log3((x^2-2):(x+1))=1

log3((x-1)•(x+1):(x+1))=1

log3(x-1)=1

Выражение loga(x)=b равно x=a^b значит,

x-1=3^1

x-1=3

x=3+1

x=4

Answer 2

To solve the equation log₃(x² - 1) = log₃(x + 1) + 1, we can start by applying logarithmic properties. In particular, we'll use the property that states if logₐ(b) = logₐ(c), then b = c.

Using this property, we can equate the arguments of the logarithms:

x² - 1 = x + 1

Now, let's solve this quadratic equation:

x² - x - 2 = 0

We can factor this equation:

(x - 2)(x + 1) = 0

Setting each factor to zero, we have:

x - 2 = 0 --> x = 2 x + 1 = 0 --> x = -1

Therefore, the equation log₃(x² - 1) = log₃(x + 1) + 1 has two solutions: x = 2 and x = -1.