how to solve the following question using logarithms?

Question

how can I use logarithms to compare a,b,c in an ascending order $$a=\frac{3^{8.7} - 3^{6.2}}{5}\\\ b=\frac{3^{11.7} - 3^{8.7}}{6} \\\ c=\frac{3^{11.7} - 3^{6.2}}{11} \\\ $$ i tried to simplify a b and c to get a constant that won't effect the compression which was in this case $3^{6.2}$ and compared a and b then a and c then calculated both b and c to rank them from highest to lowest $$\\\ a=\frac{3^{6.2}(3^{2.5} - 1)}{5}\\\ b=\frac{3^{6.2}(3^{5.5} - 3^{2.5})}{6} \\\ c=\frac{3^{6.2}(3^{5.5} - 1)}{11} $$ but the lesson is about logarithms and when I added log to a b and c I could not really simplify it down

Answer 1

Your second version of the definitions makes clear that the term subtracted is rather small compared to the first term and the three expressions are not close enough for it to matter. You can also divide out the common factor $3^{6.2}$ as that will not change the ordering. Now you can use logs to compare the difference in the power of $3$ to the difference in the denominators to find the order.

Answer 2

Hint. (Without using logarithms.)
Compare, in ascending order, the slopes of these three secants to the graph $y=3^x$