How do you solve #9^ { x ^ { 2} + 13x + 2} = 81^ { 4x + 8}#?

1 Answer
Nov 13, 2017

#x=-7,2#

Explanation:

the key is to rewrite the base numbers the same

we note

#81=9^2#

#9^(x^2+13x+2)=81^(4x+8)#

#=>9^(x^2+13x+2)=9^(2(4x+8)#

#9^(x^2+13x+2)=9^(8x+16)#

#=>x^2+13x+2=8x+16#

#:.x^2+5x-14=0#

solve by factorising

#(x+7)(x-2)=0#

#=>x=-7, 2#