SOLUTION: Not sure if this is a linear equation as it has an unknown exponent, but hope you can help with solution. Find x: {{{8 * (3/2)^(2x) = 27}}} Thank you for your help.

Algebra ->  Algebra  -> Linear-equations -> SOLUTION: Not sure if this is a linear equation as it has an unknown exponent, but hope you can help with solution. Find x: {{{8 * (3/2)^(2x) = 27}}} Thank you for your help.      Log On

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Question 15585: Not sure if this is a linear equation as it has an unknown exponent, but hope you can help with solution.
Find x:
8+%2A+%283%2F2%29%5E%282x%29+=+27
Thank you for your help.
Answer by rapaljer(4551) About Me  (Show Source):
You can put this solution on YOUR website!
In this equation, if you will divide both sides of the equation by 8, the "magic" happens!! In fact, in math, this is a "contrived" problem--one that works out in a very special way, because "someone" set it up to work out in this "special" way!! Anyway, divide both sides by 8, and see what nice things happen:

It gives you this:
8+%2A+%283%2F2%29%5E%282x%29+=+27
+%283%2F2%29%5E%282x%29+=+27%2F8

Notice that both the numerator and denominator are perfect cubes or 27 and 8. This means that this equation can also be written as this:
+%283%2F2%29%5E%282x%29+=+%283%2F2%29%5E3

If +a%5Ex+=+a%5Ey+ where the base numbers are the same, then it means that x+=+y the exponents must be equal.
+%283%2F2%29%5E%282x%29+=+%283%2F2%29%5E3 so therefore, 2x=+3 and x+=+3%2F2.

R^2 at SCC