unique solution for logarithmic syseq with parameter
Source: Moldova 2000 Grade 10 P6
April 26, 2021
algebra
Problem Statement
Find all real values of the parameter for which the system
\begin{align*}
&1+\left(4x^2-12x+9\right)^2+2^{y+2}=a\\
&\log_3\left(x^2-3x+\frac{117}4\right)+32=a+\log_3(2y+3)
\end{align*}has a unique real solution. Solve the system for these values of .