Given that \[3(4^p) = 7(6^q)\] and \[3(8^{p+1}) = 25(6^q),\] prove that \[2^p = \frac{25}{56},\] and express \(6^q\) also as the quotient of two integers.
Determine, to two significant figures, the value of \(p\).
Exponentials & Logarithms
Question
Given that \[3(4^p) = 7(6^q)\] and \[3(8^{p+1}) = 25(6^q),\] prove that \[2^p = \frac{25}{56},\] and express \(6^q\) also as the quotient of two integers.
Determine, to two significant figures, the value of \(p\).