Really Hard Logarithmic Question

Question

simplify 9^(log7)/(log3) without a calculator and showing all steps 

Answer 1

By the change of base formula, log_ab = logb/loga.

 

So, if a = 3 and b = 7, we have log7/log3 = log₃7

 

9^(log7/log3) = 9^log₃7 = (3²)^{log₃7 ₌}3^2log₃7 = 3^log₃(49) = 49   (a^log_ax = x)

 

                                              

Answer 2

9^{(log7)/(log3)}=(3²)^log₃7=3^2log₃7=3^log₃49=49