Question

Express $\log 648$ in terms off $x$ and $y$ where $\log 2=x,\log 3=y$?

Answer 1

The given term $\log 648$ can be written as $\log \left(2^3\times 3^4\right)$.

$\log \left(2^3\times 3^4\right)=\log 2^3+\log 3^4$

$=3\log 2+4\log 3$

Since, $\log 2=x$ and $\log 3=y$, then,

$\log 648=3x+4y$