Question

Lg(x+7)=lg 2+lg×(x+1)

Answer 1

Ответ:

Пошаговое объяснение:

Answer 2

To solve the equation lg(x+7) = lg(2) + lg(x+1), we need to use logarithmic properties to simplify and solve for x. Let's go through the steps:

Step 1: Use the logarithmic property log(a) + log(b) = log(a * b):

lg(x+7) = lg(2) + lg(x+1) lg(x+7) = lg(2 * (x+1))

Step 2: Use the property log(a) = log(b) if and only if a = b:

x + 7 = 2 * (x + 1)

Step 3: Distribute the 2 on the right side:

x + 7 = 2x + 2

Step 4: Move the terms with 'x' to one side and constants to the other side:

x - 2x = 2 - 7 -x = -5

Step 5: Multiply both sides by -1 to isolate 'x':

x = 5

So, the solution to the equation is x = 5. You can check this by substituting x = 5 back into the original equation to see if both sides are equal.