Question

Log4(2x+6)=log4(x-8)

Answer 1

Ответ:

корней нет

Объяснение:

log₄(2x+6)=log₄(x-8)

2x+6>0⇒x>-3

x-8>0⇒x>8

ОДЗ: x∈(8; +∞)

4) 2x+6=x-8

2x-x=-8-6

x=-14∉(8: +∞)⇒x∈∅

Answer 2

To solve the equation log₄(2x + 6) = log₄(x - 8), we need to use logarithmic properties to simplify the equation and find the value of x.

Step 1: Apply the property of logarithms that states if logₐ(b) = logₐ(c), then b = c.

log₄(2x + 6) = log₄(x - 8)

Step 2: Set the expressions inside the logarithms equal to each other.

2x + 6 = x - 8

Step 3: Solve for x.

Subtract x from both sides:

2x - x + 6 = x - x - 8

x + 6 = -8

Subtract 6 from both sides:

x + 6 - 6 = -8 - 6

x = -14

So, the solution to the equation is x = -14.