Question

Log2(4x+12x)=log2(2x+6x)

Answer 1

Пошаговое объяснение:

основания логарифмов равны, значит и подлогарифменные выражения равны:

4x + 12x = 2x + 6x

8x = 0

x = 0

Но подлогарифменное выражение не может быть равно нулю, а значит корней нет.

Answer 2

To solve the equation log2(4x + 12x) = log2(2x + 6x), we can use the properties of logarithms. One important property is that if log_a(b) = log_a(c), then b = c. In your case, both sides of the equation have the same base (log2), so we can set the expressions inside the logarithms equal to each other and solve for x:

4x + 12x = 2x + 6x

Combine like terms:

16x = 8x

Subtract 8x from both sides:

16x - 8x = 0

Simplify:

8x = 0

Now, divide both sides by 8:

x = 0

So, the solution to the equation log2(4x + 12x) = log2(2x + 6x) is x = 0.