Ask a New Question

Question


Let $x$, $y$, and $z$ be positive real numbers that satisfy
\[2 \log_x (2y) = 2 \log_{2x} (4z) = \log_{2x^4} (8yz) \neq 0.\]
The value of $xy^5 z$ can be expressed in the form $\frac{1}{2^{p/q}}$, where $p$ and $q$ are relatively prime positive integers. Find $p + q$.
9 years ago

Answers

Steve
This is discussed at

http://www.artofproblemsolving.com/community/c5h469913p2630559

click on the link that says <u>solution</u>
9 years ago
dudegum
yup can confirm steves answer, 049
4 years ago

Related Questions

You are trying out for the position of place-kicker on a professional football team. With the ball t... I need to know whether the position of the CG is higher, lower, or at the same level within the body... 35. If 1<6n<66, and n is a positive integer, what is the greatest possible value for n? A.9 B.10... What is the sum of all the positive numbers smaller than 100,000 where all digits can only be 1 or 0... You are trying out for the position of place-kicker on a professional football team. With the ball t... What does it mean when the position vs. time graph is below the x-axis? Let f(n) be the sum of the positive integer divisors of n. For how many values of n, where 1<n<25, i... If x2 + 9 = 25 what is the positive value of x Is –5,796,971 − 16,035 positive or negative? Which is an example of the positive impact of mass media on social problems? (1 point) Responses A s...
Ask a New Question
Archives Contact Us Privacy Policy Terms of Use