Solve the exponential equation by converting to a common base:

Question

Show step by step work:

27^x-16=9^7x+31

Answer 1

The common base is 3

27= 3^3 and 9= 3^2 so

(3^3)^x-16 = (3^2)^7x+31

3^ 3x-48 = 3^ 14x+62 so

3x-48 = 14x+62

-11x= 110

x=-10