Use properties of logarithms to find the exact value of each expression. Do not use a calculator.
8^log 8^5
let x = 8^log8^5
I can't see a way to get an "exact" answer.
by calculator I get appr 11963.5
are you sure the base of the log is not 8 ?
Sorry, it says
8^log(8^5)
then my above answer stands, no "exact" answer other than 8^log(8^5) itself
check:
log 8^5 = log 32768 = 4.515449...
then 8^log (8^5)
= 8^4.51449 = appr 11963.5
I would get an 'exact' answer if the base of the log at the top had been 8.
That is why I questioned your problem.
To find the exact value of the expression 8^(log 8^5), we need to simplify using properties of logarithms.
First, we note that the expression can be written as (8^log 8)^5.
Using the property log_b(b^x) = x, we can simplify further. In this case, the base of the logarithm is 8, and the exponent is log 8.
So, log 8^5 simplifies to 5.
Now, we are left with (8^log 8)^5 = 8^5.
Simplifying this, we get the exact value of the expression: 32768.
Therefore, 8^(log 8^5) is equal to 32768.