Question 102
If $$f(x) = 8x^4$$ and $$g(x) = \sqrt[3]{f(x)}$$, then find the value of $$\log_2(fog(64))$$.
Solution
To find $$\log_2(fog(64))$$, we shall first find the value of fog(64).
The value of g(64): $$\sqrt[3]{f(64)}$$, where f(64) is $$8^9$$
The cube root of the following expression would be $$8^3$$, which is the value of g(64).
Now, fog(64) is f($$8^3$$), which is $$8^{13}$$.
For the final result, $$\log_2\left(8^{13}\right)$$, which is $$\log_2\left(2^{39}\right)$$ , or 39.
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