The functions 𝑔 and ℎ are given by           𝑔⁡(𝑥)=log4⁡(2⁢𝑥)            ℎ⁡(𝑥)=(𝑒𝑥)5𝑒(1/4).(i) Solve 𝑔⁡(𝑥)=3 for values of 𝑥 in the domain of 𝑔.(ii) Solve ℎ⁡(𝑥)=𝑒(1/2) for values of 𝑥 in the domain of ℎ.

(i) To solve the equation g(x) = 3, we first substitute g(x) with its definition, which gives us log4(2x) = 3. The logarithmic equation can be rewritten in exponential form as 4^3 = 2x. Simplifying this gives 64 = 2x. Dividing both sides by 2, we find that x = 32.

(ii) To solve the equation h(x) = e^(1/2), we first substitute h(x) with its definition, which gives us (e^x)^5 * e^(1/4) = e^(1/2). Simplifying the left side gives us e^(5x + 1/4) = e^(1/2). Since the bases are equal (both are e), we can set the exponents equal to each other, which gives us 5x + 1/4 = 1/2. Solving for x, we subtract 1/4 from both sides to get 5x = 1/4, and then divide by 5 to find that x = 1/20.