02. Logarithms question bank (Maths)

If \( a, b, c \) are positive real numbers such that  
\[
a^{\log_3 7} = 27,\quad b^{\log_7 11} = 49,\quad c^{\log_{11} 25} = \sqrt{11}
\]  
The value of  
\[
a^{(\log_3 7)^2} + b^{(\log_7 11)^2} + c^{(\log_{11} 25)^2}
\]  
equals  

If \(60^a = 3\) and \(60^b = 5\), then the value of  
\[
12^{\dfrac{1 - a - b}{2(1 - b)}}
\]
equals