log2(x-2)+log2(x-3)=1

To solve the given equation, we can use the properties of logarithms.

First, we can combine the logarithms using the product rule of logarithms: log2((x-2)(x-3)) = 1

Now we can rewrite the equation using the definition of logarithms: 2^1 = (x-2)(x-3)

Simplify the left side: 2 = (x-2)(x-3)

Expand and simplify the right side: 2 = x^2 - 5x + 6

Set the equation equal to zero: x^2 - 5x + 6 - 2 = 0 x^2 - 5x + 4 = 0

Factor the quadratic equation: (x-4)(x-1) = 0

Now, set each factor to zero to find the possible values of x: x - 4 = 0 => x = 4 x - 1 = 0 => x = 1

Therefore, the solution to the equation log2(x-2) + log2(x-3) = 1 is x = 4 or x = 1.