how do you simplify log5 square root pq over 8
To simplify the expression log5(square root pq) over 8, we can use the properties of logarithms.
First, let's start by using the property of the square root inside the logarithm. The square root can be written as exponentiation with a 1/2 exponent:
log5(square root pq) = log5((pq)^(1/2))
Next, let's use the property of logarithms that allows us to bring the exponent down as a coefficient:
log5((pq)^(1/2)) = (1/2) * log5(pq)
Now we have simplified the expression to (1/2) times log5(pq) over 8:
(1/2) * log5(pq) over 8
At this point, we cannot simplify it further since the logarithm is still inside the fraction. However, if you have specific values for p and q, you can substitute those values and evaluate the expression further.