Answer:
\(F(64)=2\)
Step-by-step explanation:
Given the funtion:
\(F(x)=log_8(64)\)
We need to find the value of the function at x=64:
\(F(64)=log_8(64)= z\)
Where z is the value we are trying to find. In order to find z, let's use the definition of the base of a log:
\(log_xy=z\Rightarrow x^z=y\)
So:
\(8^z=64\)
Express \(8^z\) as:
\(2^{3z}\)
And express 64 as:
\(2^6\)
Which leads to:
\(2^{3z}=2^6\)
Equate exponents of 2 on both sides:
\(3z=6\)
Solving for z:
\(z=\frac{6}{3} =2\)
Therefore:
\(F(64)=log_8(64)= z=2\)
