Question

Log4(5x – 4) log4(5x – 1)=1

Answer 1

Система 5x-4=5x-1, 5ч-1=1.

Затем выписываем уже без системы и приводим подобные..

 

Answer 2

To solve the equation log₄(5x - 4) · log₄(5x - 1) = 1, we can use logarithmic properties to simplify the equation and then solve for x.

First, let's rewrite the equation using the property that logₐ(b) · logₐ(c) = logₐ(b · c):

log₄((5x - 4) · (5x - 1)) = 1

Next, we can use the property that logₐ(b) = c is equivalent to aᶜ = b:

4¹ = (5x - 4) · (5x - 1)

4 = (5x - 4) · (5x - 1)

Expand the right side:

4 = 25x² - 20x - 5x + 4

Combine like terms:

4 = 25x² - 25x + 4

Rearrange the equation to form a quadratic equation:

25x² - 25x = 0

Factor out 25x:

25x(x - 1) = 0

Now we have two possible solutions:

1. 25x = 0: Divide both sides by 25: x = 0

2. x - 1 = 0: Add 1 to both sides: x = 1

Therefore, the solutions to the equation log₄(5x - 4) · log₄(5x - 1) = 1 are x = 0 and x = 1.