By using the natural logarithm, we will see that the value of a is 0.33
How to get the value of a?
We know that:
h(x) = x^a
And we know that:
h(27x) = 3h(x).
We can rewrite this as:
(27x)^a = 3*(x)^a
And remember that we can distribute exponents, so the left side can be rewritten as:
(27*x)^a = (27^a)*(x^a)
Then we have:
(27^a)*(x^a) = 3*(x)^a
This means that:
27^a = 3
Now remember the rule:
ln(x^n) = n*ln(x)
If we apply the natural logarithm to both sides, we get:
ln(27^a) = ln(3)
a*ln(27) = ln(3)
a = ln(3)/ln(27) = 0.33
If you want to learn more about the natural logarithm, you can read:
https://brainly.com/question/13473114
