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equation and system of equations

Source: Romanian District Olympiad 2000, Grade X, Problem 1

September 24, 2018
equationssystem of equationsnumber theoryalgebra

Problem Statement

a) Solve the system {3y−4x=11log⁡4x+log⁡3y=3/2 \left\{\begin{matrix} 3^y-4^x=11\\ \log_4{x} +\log_3 y =3/2\end{matrix}\right.
b) Solve the equation   9^{\log_5 (x-2)} -5^{\log_9 (x+2)} = 4.
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