Question

Log_16 (5x-2)=log_16 (x+4) ришите пажалуйта с проверкой

Answer 1

основания логарифмов равны поэтому можем записать
5x-2=x+4
4x=6
x=1,5
проверим ОДЗ 5х-2>0 x>0,4 выполнено
проверка
log_16 (5*1,5-2)=log_16 (5,5)
log_16 (x+4)=log_16 (1,5+4)=log_16 (5,5)

Answer 2

To solve the equation log_16(5x-2) = log_16(x+4), we can use the property of logarithms that states that if log_a(b) = log_a(c), then b = c.

In this case, we have log_16(5x-2) = log_16(x+4). By applying the property mentioned above, we can set the expressions inside the logarithms equal to each other:

5x-2 = x+4

Now, we can solve this equation for x. Let's simplify it step by step:

1. Subtract x from both sides of the equation: 5x - x - 2 = x - x + 4 4x - 2 = 4

2. Add 2 to both sides of the equation: 4x - 2 + 2 = 4 + 2 4x = 6

3. Divide both sides of the equation by 4: (4x)/4 = 6/4 x = 3/2

Therefore, the solution to the equation log_16(5x-2) = log_16(x+4) is x = 3/2.

Let's verify this solution by substituting it back into the original equation:

log_16(5(3/2)-2) = log_16((3/2)+4)

Simplifying the left side: log_16(15/2 - 2) = log_16(11/2)

15/2 - 2 = 11/2, so the left side becomes: log_16(11/2) = log_16(11/2)

Since both sides are equal, the solution x = 3/2 is verified.

I hope this helps! Let me know if you have any further questions.