Question

How can the indicated logarithm be found? Without a calculator❓

Answer 1

I guess you're supposed to write the expression on the right in terms of $A,B,C$.

18. Notice that $729=9^3$, so

$\log_8729=\log_89^3=3\log_89=3B$

20. Notice that $\dfrac{14}3=\dfrac{42}9=\dfrac{6\times7}9$, so

$\log_8\dfrac{14}3=\log_8\dfrac{6\times7}9=\log_86+\log_87-\log_89=A+C-B$