log^8 sqrt 13/11

To evaluate the expression log^8(sqrt(13/11)), we can follow these steps:

Step 1: Simplify the expression inside the square root.
First, simplify the fraction 13/11 by dividing the numerator (13) by the denominator (11). This simplifies to 1.181818...

Step 2: Take the square root of the simplified fraction.
The square root of 1.181818... is approximately 1.086278...

Step 3: Raise the result to the power of 8.
Raising 1.086278... to the power of 8 gives us approximately 2.20477...

Step 4: Take the logarithm base 10 of the result.
The logarithm base 10 of approximately 2.20477... is approximately 0.34217...

So, log^8(sqrt(13/11)) is approximately equal to 0.34217...