# SOLUTION: given log3=x and log5=y express log &#8730;(3/5)in terms of x and y

Algebra ->  Algebra  -> Logarithm Solvers, Trainers and Word Problems -> SOLUTION: given log3=x and log5=y express log &#8730;(3/5)in terms of x and y       Log On

 Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help! Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

 Algebra: Logarithm Solvers Lessons Answers archive Quiz In Depth

 Question 423397: given log3=x and log5=y express log √(3/5)in terms of x and y Answer by Theo(3464)   (Show Source): You can put this solution on YOUR website!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.