Final answer:
The answer for the equation is X=2.
Step-by-step explanation:
To solve the logarithmic equation log11(x-4) - log11(x-2) = 2, we can use the property of logarithms that states the logarithm of the quotient of two numbers is equal to the difference of their logarithms. Applying this property, we have:
log11((x-4)/(x-2)) = 2
Next, we can rewrite the equation in exponential form:
(x-4)/(x-2) = 11^2
Simplifying the expression on the right side gives:
(x-4)/(x-2) = 121
To solve for x, we can cross multiply:
121(x-2) = x-4
Expanding and rearranging the equation, we get:
121x - 242 = x - 4
Combining like terms, we have:
120x = 238
Finally, dividing both sides by 120 gives:
x = 2