given f(x)=log[4]x, then f(8) equals?

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Given f(x) = log4 (x)

We need to find f(8)

We will substitute with x= 8 into the equation.

==> f(8) = log4 (8)

Now we will rewrite as a product.

==> g(8) = log4 (2*4)

But we know that log4 2*4 = log4 2 + log4 4

But log4 4 = 1

==> log4 8 = log4 2 + 1

Now we will rewrite log4 2 = log2 2 / log2 4 = 1/log2 2^2 = 1/2log2 2 = 1/2

==> log4 8 = 1/2 + 1 = 3/2

**Then we conclude that f(8) = log4 8 = 3/2**

We have f(x) = log (4) x.

f(8) = log(4) 8

=> log(4) 2^3

=> log(4) 4^(3/2)

we use the relation log a^n = n*log a

=> (3/2) log(4) 4

use log (a) a = 1

=> 3/2

**The required result is 3/2**

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