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.

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:

Thank you for your help.
Answer by rapaljer(4671) (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:

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:

If where the base numbers are the same, then it means that the exponents must be equal.
so therefore, and .

R^2 at SCC

RELATED QUESTIONS
I am trying to solve an equation with fractions. This is the problem 2x over x^2+6x+8 (answered by stanbon)

SO im not sure what these are called but this is what it says... Solve these systems of... (answered by ankor@dixie-net.com)

Hello, I'm taking Calculus online and have a homework problem I'm having trouble with. (answered by Alan3354)

Hello, please help me solve this problem. A committee of 4 people is to be form from 6... (answered by stanbon)

hi!! please help me i already answered it but I'm just checking if my answer is correct... (answered by stanbon)

I tried to find an equation with the the unknown amount of coins but could not find one.... (answered by stanbon,ikleyn,MathTherapy)

I'm very much stuck on this problem. I'm not sure if this is in the right section, but I (answered by mananth)

Thanks so much for all your help . After see the problem solve i try to work on them to... (answered by stanbon)

{{{(x^2 + 2) d^2y/dx^2 + 3x dy/dx - y = 0}}} (tried to write this as simply (x^2 +... (answered by Edwin McCravy)