# calculate log 8 (sqrt8^20)

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log 8 (sqrt8^20)

Let us simplify:

log 8 (sqrt(8^20)= 20 log 8 (sqrt(8)

= 20 log 8 (8)^1/2

= 20*(1/2) log 8 (8)

= 10*1

= 10

The answer is 10.

First, let's calculate sqrt 8^20 = (8^2*10)^(1/2) = 8^(2*10/2) = 8^10

Now, we'll calculate :

log 8 (8^10)

We'll use the power property of logarithms:

log 8 (8^10) = 10 log 8 (8), but log 8 (8) = 1

10 log 8 (8) = 10*1 = 10

**log 8 (sqrt8^20) = 10**

To find log8 (sqrt l (8^20).

Solution:

sqrt x^m = (x^m)^(1/2) = x^(m/2), by index law.

So sqrt8^20 = 8^(20/2) = 8^10.

log a (a^n ) = n. By definition of logarithm.

Therefore, log8 (sqrt 8^20) = log8 (8^(20/(2)) = log8 (8^10) = 10.