The functions 𝑔 and ℎ are given by          𝑔⁡(𝑥)=log5⁡(4⁢𝑥-2)          ℎ⁡(𝑥)=sin-1⁡(8⁢𝑥).(i) Solve 𝑔⁡(𝑥)=3 for values of 𝑥 in the domain of 𝑔.

To solve the equation g(x) = 3, we first need to understand that g(x) = log5(4x - 2).

So, we have:

log5(4x - 2) = 3

The next step is to convert the logarithmic equation into an exponential one. The base of the logarithm becomes the base of the power, the right hand side of the equation becomes the power, and the argument of the logarithm becomes the result. So, we get:

5^3 = 4x - 2

Solving this gives us:

125 = 4x - 2

Next, we isolate x by adding 2 to both sides of the equation:

127 = 4x

Finally, we divide both sides by 4 to solve for x:

x = 127/4 = 31.75

So, the solution to the equation g(x) = 3 is x = 31.75.