Final answer:
The equation of the function g(x) is g(x) = 2 * log5(x + 8) + 3. It is obtained by stretching the graph by a factor of 2, shifting it to the left by 8 units, and shifting it up by 3 units.
Step-by-step explanation:
The equation of the function g(x) described above is:
g(x) = 2 * log5(x + 8) + 3
To stretch the graph vertically by a factor of 2, we multiply the function by 2. To shift the graph to the left by 8 units, we subtract 8 from the x-values. And to shift the graph up by 3 units, we add 3 to the function.
For example, if we want to find the value of g(2), we substitute x = 2 into the equation:
g(2) = 2 * log5(2 + 8) + 3
g(2) = 2 * log5(10) + 3
g(2) = 2 * 1 + 3
g(2) = 5