Let r = log6 17, s = log4 17, t = log6 4.
Write the following expressions in terms of r, s, and/or t. The change of base formula may be helpful in finding some of these logarithms.
By the change of base formula, we have that:
$\displaystyle \log_{16}17 = \frac {\log_4 17}{\log_4 16} = \frac s{2}$
we have:
$\displaystyle \log_4 17 \left( 6^{\log_{36} 4}\right) = s \left( 6^{\frac {\log_6 4}{\log_6 36}} \right)$ ....by the change of base formula
So we get: $\displaystyle \log_4 17 \left( 6^{\log_{36} 4}\right) = s \left( 6^{\frac t{2}} \right)$