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

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Answer 1 · 2017-09-15T08:53:15

# x=13/2.#

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.