Question

If 25^log3_9+3^log25_5=4^log14_x then x=​

Answer 1

Answer:

x = 4

Step-by-step explanation:

In 25^log3_9, base 9 is 3^2 so by property of log,

it becomes,

25^(1/2*log3_3)

thus, 25^1/2 = 5 (bcoz log3_3 = 1).........(1)

Similarly,

3^log25_5 = 3^2 = 9...........(2)

from (1) and (2) , we get ,

5 + 9 = 14

Now on the other side,

logarithmic property says : if number and base of powered log is same then logarithmic function is the answer.

so for the answer to be 14, the base x had to be equal to 4.