Suppose 43^(3*log13(56)) = 56^(x*log11(43)), where x = logb(n) Compute the pair of positive integers (b, n) that satisfies this equation, where b is the minimum value greater than ten.

Question

*note the log in the exponent is base 13, and base 11 respectively while what's inside the bracket is the argument

Answer 1

x = 3log₁₃11

Take log13 of both sides.
3log13(56) * log13(43) = x*log11(43) * log13(56)
x = 3log13(56) * log13(43) / log11(43)*log13(56)
= 3 * log13(43)/log11(43)
Now recall your change-of-base formula.