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

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> 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      Log On


   

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) About Me  (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: %289%5E%282x%29%29%2A%2827%5E%28x-3%29%29=1%2F9 simplifies to 9%5E%282%2Ax%29%2A27%5E%28x-3%29-1%2F9=0
  • Text form: (9^(2x))*(27^(x-3))=1/9 simplifies to 9^(2*x)*27^(x-3)-1/9=0
  • Cartoon (animation) form: simplify_cartoon%28+%289%5E%282x%29%29%2A%2827%5E%28x-3%29%29=1%2F9+%29
    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 highlight_red%28+%28highlight_red%28+9%5E%282%2Ax%29+%29%29%2A%2827%5E%28x-3%29%29+%29=1%2F9.
Remove unneeded parentheses around factor highlight_red%28+9%5E%282%2Ax%29+%29
It becomes highlight_green%28+9%5E%282%2Ax%29+%29%2A%2827%5E%28x-3%29%29=1%2F9.
Look at highlight_red%28+9%5E%282%2Ax%29%2A%28highlight_red%28+27%5E%28x-3%29+%29%29+%29=1%2F9.
Remove unneeded parentheses around factor highlight_red%28+27%5E%28x-3%29+%29
It becomes 9%5E%282%2Ax%29%2Ahighlight_green%28+27%5E%28x-3%29+%29=1%2F9.
Look at 9%5E%282%2Ax%29%2A27%5E%28x-3%29=highlight_red%28+1%2F9+%29.
Moved these terms to the left highlight_green%28+-1%2F9+%29
It becomes 9%5E%282%2Ax%29%2A27%5E%28x-3%29-highlight_green%28+1%2F9+%29=0.
Result: 9%5E%282%2Ax%29%2A27%5E%28x-3%29-1%2F9=0

Universal Simplifier and Solver


Done!

Answer by HyperBrain(694) About Me  (Show Source):
You can put this solution on YOUR website!
%289%5E%282x%29%29%2A%2827%5E%28x-3%29%29=1%2F9+
%28%289%5E2%29%5Ex%29%2A%2827%5Ex%2F27%5E3%29=1%2F9
81%5Ex%2A%2827%5Ex%2F27%5E3%29=1%2F9
log+%28%28+81%5Ex+%2A+%2827%5Ex%2F27%5E3%29%29%29=log+%281%2F9%29
x+log%2881%29%2B+x+log%2827%29-3+log%2827%29=log+%281%29-+log%289%29
x+log%2881%29%2B+x+log%2827%29-3+log%2827%29=-+log%289%29_-----------log 1 =0!
%281.90848501887865%2Ax%29%2B%281.4313637415899%2Ax%29-4.29409129247696=-0.9542450943932
3.3398487604685503%2Ax=3.3398461980837597
x=1
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) About Me  (Show Source):
You can put this solution on YOUR website!
%289%5E%282x%29%29%2A%2827%5E%28x-3%29%29=1%2F9
Use the exponentiation rules
%28x%5Em%29%5En=x%5E%28m%2An%29
%28x%5Em%29%2A%28x%5En%29=x%2A%28m%2Bn%29
Let's start.
%28%283%5E2%29%5E%282x%29%2A%283%5E3%29%5E%28x-3%29%29=3%5E%28-2%29+Convert to the same base, 3.
3%5E%284x%29%2A%283%5E%283%28x-3%29%29%29=3%5E%28-2%29+Use the rules.
3%5E%284x%2B%283%28x-3%29%29%29=3%5E%28-2%29+Simplify.
4x%2B3%28x-3%29=-2Inverse function.
4x%2B3x-9=-2Distribute.
7x-9=-2Additive inverse.
7x=7Multiplicative inverse.
x=1
Verify the solution.
%289%5E%282x%29%29%2A%2827%5E%28x-3%29%29=1%2F9
%289%5E%282%29%29%2A%2827%5E%281-3%29%29=1%2F9
%2881%2F729%29=1%2F9
%281%2F9%29=1%2F9
Good answer.

Answer by bimanewton(8) About Me  (Show Source):
You can put this solution on YOUR website!
%289%5E%282x%29%29%2A%2827%5E%28x-3%29%29=1%2F9
%283%5E%284x%29%29%2A%283%5E%283x-9%29%29=%283%5E%28-2%29%29
%283%5E%287x-9%29%29=%283%5E%28-2%29%29
you can forget 3 because it has same
so
7x-9=-2
7x=7
x=1
cheers