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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 findĀ $$\log_2(fog(64))$$, we shall first find the value ofĀ fog(64).Ā
The value of g(64): $$\sqrt[3]{f(64)}$$, where f(64) isĀ $$8^9$$
The cube root of the following expression would beĀ $$8^3$$, which is the value of g(64).
Now, fog(64) is f($$8^3$$), which isĀ $$8^{13}$$.
For the final result,Ā $$\log_2\left(8^{13}\right)$$, which isĀ $$\log_2\left(2^{39}\right)$$ , or 39.Ā
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