MathDB

Logarithms in x,y,z

Source: 2012 AIME I Problem 9

March 16, 2012

logarithmsnumber theoryrelatively primeAMC

Problem Statement

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^5z

can be expressed in the form

\frac{1}{2^{p/q}}

, where

p

and

q

are relatively prime integers. Find

p+q

.

Back to Problems View on AoPS