I assume you meant:
9^(x+1)=27^(x+4) now not that 9=3^2 and 27=3^3 then you have:
(3^2)^(x+1)=(3^3)^(x+4)
And remember the rule of exponents raised to another exponent:
(a^b)^c = a^(b*c) so what the above equals is:
3^(2(x+1))=3^(3(x+4)) which is equal to:
3^(2x+2)=3^(3x+12) if you take the natural log of both sides you get:
(2x+2)ln3=(3x+12)ln3 now divide both sides by ln3 to get:
2x+2=3x+12 subtract 3x from both sides
-x+2=12 subtract 2 from both sides
-x=10 divide both sides by -1
x=-10
check...
9^(-10+1)=27^(-10+4)
9^(-9)=27^(-6) and again remembering that 9=3^2 and 27=3^3 you have:
3^2^(-9)=3^3^(-6)
3^-18=3^-18
correct.
