Final answer:
To solve the equation log_(3)(x+6)-log_(3)(x-8)=3, we can use the property of logarithms and convert the equation to exponential form. Solving for x gives us x = 8.54.
Step-by-step explanation:
To solve the equation log3(x+6)-log3(x-8)=3, we can use the property of logarithms that states log(a) - log(b) = log(a/b). Applying this property, we can rewrite the equation as log3((x+6)/(x-8))=3.
Next, we can convert the equation to exponential form by raising both sides to the power of 3, resulting in (x+6)/(x-8) = 3^3 = 27.
Now, we can solve for x by cross-multiplying and simplifying the equation: x+6 = 27(x-8). After that, we can solve for x: x+6 = 27x-216, 26x = 222, and finally, x = 8.54.