Find x if 2 log x =log (x+6)

Answer 1

To solve this equation, we can use the property of logarithms that states: log(a) + log(b) = log(a*b) and log(a) - log(b) = log(a/b).

Given the equation: 2 log x = log (x+6)

We can rewrite it using the property: log x² = log (x+6)

Now, we can drop the logarithm from both sides, as the logarithm of some number is equal only if the numbers are equal: x² = x+6

Rearranging this equation, we get a quadratic equation: x² - x - 6 = 0

Now, we can factor this quadratic equation: (x - 3)(x + 2) = 0

Setting each factor to 0 gives us the possible solutions: x - 3 = 0 or x + 2 = 0

Solving these equations, we get: x = 3 or x = -2

Therefore, the solutions to the equation 2 log x = log (x+6) are x = 3 or x = -2.