Question 423397
log(3) = x
log(5) = y
log(sqrt(3/5) = ?????


let a = 3/5


log(sqrt(3/5) = log(sqrt(a) = log(a^(1/2) = 1/2 * log(a)


substituting for a, we get:


log(sqrt(3/5)) = 1/2 * log(3/5)


since we know that log(3/5) = log(3) - log(5), then this equation becomes:


log(sqrt(3/5)) = 1/2 * (log(3) - log(5))


since we know that log(3) = x and log(5) = y, then this equation becomes:


log(sqrt(3/5)) = 1/2 * (x - y)


if you solve for the original equation and the final equation, you will see that the log of each will be equal to -.110924375


this confirms that the conversion of the formula is correct.


to solve for the original equation, you take the square root of (3/5) and you take the log of it to get -.110924375


to solve for the final equation, you take the log(3) and subtract the log(5) from it and then multiply the result by 1/2 to get -.110924375.


your intermediate answer is that:


log(sqrt(3/5)) = (1/2) * (log(3) - log(5))


your final answer is that:


log(sqrt(3/5)) = (1/2) * (x - y)


this is because x = log(3) and y = log(5) which was given.