How do you evaluate 9^ { 4x - 5} = 27^ { 2x + 1}?

1 Answer
Sep 15, 2017

x=13/2.

Explanation:

Given the eqn., 9^(4x-5)=27^(2x+1).

:. (3^2)^(4x-5)=(3^3)^(2x+1).

:. 3^{2xx(4x-5)}=3^{3xx(2x+1)}..........[because, (a^m)^n=a^(mn)],

:. {2xx(4x-5)}={3xx(2x+1)}............................................. [because, a^m=a^n rArr m=n],

:. 8x-10=6x+3.

:. 8x-6x=3+10.

:. 2x=13.

:. x=13/2.

This root also satisfies the given eqn.

:. x=13/2, is the Soln.