Question

Given F(x) = log8 x, find F(64). ...?

Answer 1

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:

$F(64)=log_8(64)= z=2$

Answer 2

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Below is the solution:


f(64) = log8 64 
= log8 8^2 
= 2 log8 8 
= 2