Question

Log2(8-x)=2log2(4+x)

Answer 1

Чуть-чуть пример не правельный (создателя).

должно выполниться равенство 2(4-x)=(2^5)^2

упрощая получим

8-2x=32^2

x=-508

Answer 2

To solve the equation log2(8 - x) = 2log2(4 + x), we'll need to apply logarithmic properties and algebraic manipulations to simplify and isolate the variable x. Let's go through the steps:

Step 1: Apply the power rule of logarithms to the right side of the equation: log2(8 - x) = log2((4 + x)^2)

Step 2: Remove the logarithm on both sides using the property that if logb(a) = logb(c), then a = c: 8 - x = (4 + x)^2

Step 3: Expand the right side: 8 - x = 16 + 8x + x^2

Step 4: Rearrange the equation by bringing all terms to one side: x^2 + 9x + 8 - 16 = 0

Step 5: Simplify: x^2 + 9x - 8 = 0

Step 6: Factorize the quadratic equation: (x + 8)(x - 1) = 0

Step 7: Set each factor equal to zero and solve for x: x + 8 = 0 --> x = -8 x - 1 = 0 --> x = 1

Therefore, the equation log2(8 - x) = 2log2(4 + x) has two solutions: x = -8 and x = 1.