9^x+1=27^x+4 what does x equal?

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.