Hi,

If $\displaystyle \log_9 x = a$ and $\displaystyle \log_3 y = b$, express $\displaystyle xy$ and $\displaystyle \frac{x}{y}$ as powers of $\displaystyle 3$.

If $\displaystyle xy = 243$ and $\displaystyle \frac{x}{y} = 3$, calculate $\displaystyle a$ and $\displaystyle b$.

I got the expression part but not the calculation:

$\displaystyle \log_9 x = a,\,\,\,\,\,\,\,\,\,\,\log_3 y = b$

$\displaystyle x = 9^a = 3^{2a}\,\,\,\,\,\,\,\,y = 3^b$

$\displaystyle xy = 3^{2a} \times 3^b$

$\displaystyle xy = 3^{2a + b}$

$\displaystyle \frac{x}{y} = \frac{3^{2a}}{3^b}$

$\displaystyle = 3^{2a - b}$