9^x(-2)+3^3(x)=81 i need help

If you mean

(9^x)^(-2) + (3^3)^x = 81
then you have

3^(-4x) + 3^(3x) = 81
if u = 3^x, then you have

1/u^4 + u^3 = 81

I'm sorry, but I don't see any algebraic solution. you sure there's no typo? Wolframalpha gets this:

http://www.wolframalpha.com/input/?i=3^%28-4x%29+%2B+3^%283x%29+%3D+81

steve can logarithm work 4 dat

I did similar what Steve did, and agree with him

Steve asked you to improve your typing of the equation, but this does not change things.

I will assume you meant:
9^(-2x) + 3^(3x) = 81
which becomes
3^(-4x) + 3^(3x) = 81
(3^-x)^4 + (3^-x)^-3 = 81
let 3^-x = t
so we have:
t^4+ t^-3 = 81
times t^3 for everybody
t^7 + 1 = 81t^3

tough to solve, unless we use something like Wolfram
http://www.wolframalpha.com/input/?i=t%5E7+%2B+1+%3D+81t%5E3

notice t = appr 3 or t = appr -3 are solutions to our last equation,
so 3^-x = 3 = 3^1
x = -1
similarly x = appr +1

somehow I don't think that is what you meant.

yes reiny daz the question i jus decided to include bracket in it,reiny u got me confuse how come 3^x become 3^-x,but what if i use logarithm can it work?

You must be referring to the 2nd term of

(3^-x)^4 + (3^-x)^-3 = 81

notice in the previous line it was 3^(3x)
which is (3^x)^3 or (3^(-x))^-3

Steve substituted 3^x, I substituted 3^-x,
our equations reflect that

No, logs will not work here, since you have to take the log of a sum, and we have no formulas to take care of log (A + B)

To solve this equation, we can follow these steps:

Step 1: Simplify the equation.
9^x * (-2) + 3^3 * x = 81

Step 2: Evaluate exponents.
(-2) * 9^x + 27x = 81

Step 3: Combine like terms.
-2 * 9^x + 27x = 81

Step 4: Move the constant term to the other side of the equation.
-2 * 9^x = 81 - 27x

Step 5: Divide both sides by -2 to get rid of the coefficient.
9^x = (81 - 27x) / -2

Now, let's simplify the right side of the equation further.

Step 6: Divide both terms by -2.
9^x = -81 / 2 + 27x / 2

Step 7: Simplify the terms.
9^x = -81/2 + 27x/2

Step 8: Find the common denominator, which is 2.
9^x = (-81 + 27x) / 2

Now, depending on what you would like to solve for, there are a few possible routes:

Route 1: Solve for x using logarithmic functions:
Take the logarithm of both sides of the equation, either natural logarithm (ln) or logarithm base 10 (log).
ln(9^x) = ln((-81 + 27x) / 2)
x * ln(9) = ln((-81 + 27x) / 2)
x = ln((-81 + 27x) / 2) / ln(9)

Route 2: Solve for x using numerical methods:
One way is to plot the left side of the equation: 9^x, and the right side of the equation: (-81 + 27x) / 2, on a graph and find their point of intersection.

Route 3: Solve for x using iterative methods:
You can use iterative methods like the Newton-Raphson method or bisection method to approximate the value of x which satisfies the equation.

Note that this equation may not have an exact solution or may have multiple solutions, so numerical or iterative methods might be required.