Final answer:
To solve the logarithmic equations, we isolate the logarithm, rewrite it in exponential form, and then solve for x. For the first equation, x equals 1, and for the second equation, x equals 5.
Step-by-step explanation:
To solve the logarithmic equation log12(7x+11)+3=5, we first subtract 3 from both sides to isolate the logarithm. This gives us log12(7x+11)=2. Next, we rewrite the equation in exponential form by raising the base 12 to the power of 2, which gives us 122=7x+11. Solving for x, we subtract 11 from both sides and divide by 7, giving us an answer of x = 1.
Similarly, to solve the logarithmic equation log2(x-4)+log2(x+2)=4, we use the property of logarithms that states log(a) + log(b) = log(a * b). We rewrite the equation as log2((x-4)(x+2))=4. Then, we rewrite it in exponential form as 24=(x-4)(x+2). Simplifying the right side and solving for x gives us x = 5.