SOLUTION: Hi there, I'm completely stumped. I need to solve for X: (9^(2x))*(27^(x-3))=1/9 I graphed it, and know that the answer SHOULD be -11, but I need to see HOW to do the pr

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Question 104905: Hi there,
I'm completely stumped. I need to solve for X:
(9^(2x))*(27^(x-3))=1/9
I graphed it, and know that the answer SHOULD be -11, but I need to see HOW to do the problem.
Thank you,
Brad Easler
Found 4 solutions by duggie, HyperBrain, Fombitz, bimanewton:
Answer by duggie(26)   (Show Source): You can put this solution on YOUR website!
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Graphical form: simplifies to
  • Text form: (9^(2x))*(27^(x-3))=1/9 simplifies to 9^(2*x)*27^(x-3)-1/9=0
  • Cartoon (animation) form:
    For tutors: simplify_cartoon( (9^(2x))*(27^(x-3))=1/9 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at .
Remove unneeded parentheses around factor highlight_red%28+9%5E%282%2Ax%29+%29
It becomes .
Look at .
Remove unneeded parentheses around factor highlight_red%28+27%5E%28x-3%29+%29
It becomes .
Look at .
Moved these terms to the left highlight_green%28+-1%2F9+%29
It becomes .
Result:

Universal Simplifier and Solver


Done!
Answer by HyperBrain(694)   (Show Source): You can put this solution on YOUR website!





_-----------log 1 =0!



NOw you got it. I don't like to cheat anyone. The result really is x=0.999999232784184. But, it is extremely close to 1! You can't deny it! And, trying 1 as a result, it worked!

Power up,
HyperBrain!
Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!

Use the exponentiation rules


Let's start.
Convert to the same base, 3.
Use the rules.
Simplify.
Inverse function.
Distribute.
Additive inverse.
Multiplicative inverse.

Verify the solution.




Good answer.
Answer by bimanewton(8)   (Show Source): You can put this solution on YOUR website!



you can forget 3 because it has same
so



cheers
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