SOLUTION: solve for x in the equation ∛(〖81〗^2 )/√(〖27〗^x )=9

Algebra ->  Finance -> SOLUTION: solve for x in the equation ∛(〖81〗^2 )/√(〖27〗^x )=9      Log On


   

Question 1195385: solve for x in the equation ∛(〖81〗^2 )/√(〖27〗^x )=9
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


root%283%2C%2881%5E2+%29%29%2Froot%282%2C%2827%5Ex+%29%29=9

Rewrite using powers of 3:

root%283%2C%28%283%5E4%29%5E2+%29%29%2Froot%282%2C%28%283%5E3%29%5Ex+%29%29=3%5E2

Use the power to a power rule: %28x%5Ea%29%5Eb=x%5E%28ab%29

root%283%2C%283%5E8+%29%29%2Froot%282%2C%283%5E%283x%29+%29%29=3%5E2

Rewrite using fractional exponents:

%283%5E8%29%5E%281%2F3%29%2F%283%5E%283x%29%29%5E%281%2F2%29=3%5E2

Use the power to a power rule again:
%283%5E%288%2F3%29%29%2F%283%5E%283x%2F2%29%29=3%5E2

Clear fractions:

%283%5E%288%2F3%29%29=%283%5E2%29%283%5E%283x%2F2%29%29

Multiply on the right (same base, so add the exponents):

%283%5E%288%2F3%29%29=3%5E%282%2B3x%2F2%29

The bases are the same, so the exponents are the same:

8%2F3=2%2B3x%2F2

Clear fractions (multiply by the LCD, 6):

16=12%2B9x
9x=4
x=4%2F9

ANSWER: x = 4/9

Note that the sequence of operations could be in many different orders; or possibly grouped to perform more than one operation at a time.

I chose to take small steps in an arbitrary order....